Omni Calculator
omnicalculator.com › math › log-2
Log Base 2 Calculator
December 17, 2025 - The log base 2 calculator quickly computes the value of the logarithm function with base two, i.e., log₂(x) for arbitrary (positive) x.
Reddit
reddit.com › r/mathhelp › log base .5 of .2 = log base 2 of 5
r/MathHelp on Reddit: Log base .5 of .2 = Log base 2 of 5
December 3, 2020 -
First off, I don't know how to do subscripts, so I'm sorry
Secondly... What??? I've been trying to wrap my head around this for a bit, but the best I can think of is that they would switch places if they were decimals, so I tried that, but nope. Log base .6 of .2 is some fraction, and same with almost every other decimal base of .2, and I honestly can't understand that at all
Please help
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I had a little think and came up with the following. You will need to know that log(ax )=xlog(a) and that log_a (b) = 1/log_b (a). Start with the left hand side but use fraction notation. Since 0.2=1/5=5-1 we can say that log_0.5 (0.2)= -log_0.5 (5). This is now 1/-log_5 (0.5) (using the second rule from above). Now using 0.5=1/2=2-1 ; we have 1/- - log_5 (2). This is log_2 (5). Hopefully you can follow those steps. It’s not the clearest when typed out. The reason it works here is because 0.5=1/2 and 0.2=1/5, notice the 2’s and 5’s in both decimal and fraction representation. That’s why it doesn’t work for other decimals.
A method for approximating log(5) (base 2) ...
memorize your fractional powers of ten and this kind of thing is easy (I went over an easy way to get the fractional powers of ten in this comment) Anyway, using that method, 10^0.7 = 5.01 . So log10(5.01) = 0.7 and 10^0.3 = 1.99 so log2(5) = 1/log10(2)*log10(5) = 1/0.3*0.7 = 0.7/0.3 = 7/3 . More on reddit.com
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June 1, 2015math - How to compute floor(log2(5**x)) without floating point arithmetic or long integer computation - Stack Overflow
For each integer n in [1,N], compute ... power of 5, x, that such that 2n is no greater than 5x. Store a mapping between x and n. ... yeah, with x <= 100, it shouldnt be hard. the ditgis after 5 digits, don't matter after multiplication, so we can just perform ~5 digit integer multiplication. interested in seeing other approaches ... As you correctly note, log2(5**x) == x ... More on stackoverflow.com
Logarithm question: I can't figure out how (log5)^2+(log2)^2+2log2log5 equals 1 | Free Math Help Forum
I am pleased to to see that that ... the end of an answer matters. ... You could solve the problem as follows: Let x=log5 and y = log2. Then the problem becomes x^2 + y^2 + 2xy = (x+y)^2 Now x+y = log 5 + log2 = log(5*2) = log 10 = 1. So, x^2 + y^2 + 2xy = (x+y)^2= (1)^2 = 1 ... Yes thanks. I’ve got it now. I appear to have started an interesting conversation. My textbooks use log to mean log base 10 and ln ... More on freemathhelp.com
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What is log base 2?
Log base 2, also known as the binary logarithm (written as log₂(x) or lb(x)), is the power to which 2 must be raised to obtain a given number. For example, log₂(8) = 3 because 2³ = 8. It is extensively used in computer science, information theory, and binary computations.
miniwebtool.com
miniwebtool.com › home page › math › logarithm calculators › log base 2 calculator
Log Base 2 Calculator - Binary Logarithm Calculator with Step-by-Step ...
How do you calculate log base 2?
To calculate log₂(x): (1) If x is a power of 2, count how many times you multiply 2 to get x. (2) For other numbers, use the change of base formula: log₂(x) = ln(x) / ln(2) or log₂(x) = log₁₀(x) / log₁₀(2). For example, log₂(64) = 6 because 2⁶ = 64, and log₂(10) ≈ 3.32193 using the formula.
miniwebtool.com
miniwebtool.com › home page › math › logarithm calculators › log base 2 calculator
Log Base 2 Calculator - Binary Logarithm Calculator with Step-by-Step ...
How do I calculate the logarithm in base 2?
To calculate the logarithm in base 2, you probably need a calculator. However, if you know the result of the natural logarithm or the base 10 logarithm of the same argument, you can follow these easy steps to find the result. For a number x:
-
Find the result of either
log10(x)orln(x). -
Divide the result of the previous step by the corresponding value between:
-
log10(2) = 0.30103; or -
ln(2) = 0.693147.
-
-
The result of the division is
log2(x).
omnicalculator.com
omnicalculator.com › math › log-2
Log Base 2 Calculator
Videos
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Proof that Log base 2 of 5 is irrational! - YouTube
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Prove that log 2 with base 5 is an irrational number || Real Analysis ...
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Prove that log 5 base 2 is an irrational number . - YouTube
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Solve -2log_5 (7x)=2 - YouTube
Quora
quora.com › How-is-log-5-log-2-equal-to-log-base-2-of-5
How is log 5/log 2 equal to log(base)2(of)5? - Quora
For log 5/log2 to be log base 2 of 5, 2^(log 5/log 2) would have to equal 5. Take a natural log of both sides of the equation and remember that log(a^b)=b log a. The left side becomes log(2^(log 5/log 2)). Using 2 as a and log 5/log 2 as b, ...
Calculator.net
calculator.net › home › math › log calculator
Log Calculator
If there is an exponent in the argument of a logarithm, the exponent can be pulled out of the logarithm and multiplied. logbxy = y × logbx EX: log(26) = 6 × log(2) = 1.806 · It is also possible to change the base of the logarithm using the following rule.
Answers
math.answers.com › math-and-arithmetic › What_is_log2-log5
What is log2-log5? - Answers
August 2, 2025 - However, if you meant ( \log_2(5) ), it represents the logarithm of 5 with base 2, which can be calculated using the change of base formula: ( \log_2(5) = \frac{\log_{10}(5)}{\log_{10}(2)} ) or ( \log_2(5) = \frac{\ln(5)}{\ln(2)} ). If you clarify ...
Mathway
mathway.com › popular-problems › Algebra › 203966
Evaluate log base 2 of 5 | Mathway
Evaluate log base 2 of 5 · Step 1 · The change of base rule can be used if and are greater than and not equal to , and is greater than . Step 2 · Substitute in values for the variables in the change of base formula, using . Step 3 · The result can be shown in multiple forms.
Mathway
mathway.com › popular-problems › Algebra › 887890
Solve for x log base 2 of x=5 | Mathway
Solve for x log base 2 of x=5 · Step 1 · Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to . Step 2 · Solve for . Tap for more steps... Step 2.1 · Rewrite the equation as . Step 2.2 · Raise to the power of .
MiniWebtool
miniwebtool.com › home page › math › logarithm calculators › log base 2 calculator
Log Base 2 Calculator - Binary Logarithm Calculator with Step-by-Step Solutions
December 27, 2025 - Powers of 2 produce exact integer logarithms: log₂(256) = 8 exactly. Yes, log₂(x) is negative when 0 < x < 1. For example, log₂(0.5) = -1 because 2⁻¹ = 0.5, and log₂(0.25) = -2 because 2⁻² = 0.25.
Reddit
reddit.com › r/math › a method for approximating log(5) (base 2) ...
r/math on Reddit: A method for approximating log(5) (base 2) ...
June 1, 2015 -
I was fiddling around with log(5) (the logarithm is of base 2) , trying to find a sharp bound for it using elementary methods .
log(5) = log(5 * 2k / 2k ) = log(10 * 2k-1 ) - k , now for k=11 , we have log(5)=log(10*1024)-11 , but 1024>1000=103 : log(5)>log(104 )-11 = 4(1+log(5))-11 or
log(5) < 7/3
Can this method be generalized ? If we pick a bigger k can we get a better bound by using the same method (finding a power of 10 that is a bit smaller than 2k-1 ) ?
Mathway
mathway.com › popular-problems › Algebra › 206207
Evaluate log base 5 of 2 | Mathway
Evaluate log base 5 of 2 · Step 1 · The change of base rule can be used if and are greater than and not equal to , and is greater than . Step 2 · Substitute in values for the variables in the change of base formula, using . Step 3 · The result can be shown in multiple forms.
Symbolab
symbolab.com › calculators › math › log base 2 calculator
Log Base 2 Calculator - Symbolab
A Log Base 2 Calculator, also known as a Binary Logarithm Calculator or simply log2 calculator, is an efficient mathematical tool used for calculating logarithms with base 2. It handles computations related to the exponent, or the power to which the base number (2, in this case) must be raised in order to get a specific value. In other words, it determines the index or the exponent required for the base (2) to equal a given number. The concept of binary logarithms is crucial in various disciplines, such as computer science, digital systems and communications, information theory, coding, and cryptography.
Logarithm Calculator
logcalculator.net
Logarithm Calculator log(x)
For example, 23 = 8 ⇒ log2 8 ... one to exponentiation. Unfortunately, not all logarithms can be calculated that easily. For example, finding log2 5 ......
Logarithm Calculator
logcalculator.net › log-2
Log base 2 Calculator Log2
Log base 2 calculator finds the log function result in base two. Calculate the log2(x) logarithm of a real number, find log base 2 of a number.
Top answer 1 of 3
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As you correctly note, log2(5**x) == x * log2(5). log2(5) is a constant, which can be approximated to 2.3219281.
However, floats aren't allowed per the question. Not an issue!
log2_5 = 23219281;
scale = 10000000; // note log2_5/scale is the actual value
result = x * log2_5;
output = (result - (result % scale)) / scale;
By reducing result by result % scale, dividing it by scale will be an integer division, not a float.
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for a simple, efficient and mathematically elegant way...
floor(x*log2(5))
Since x has integer values 1 to 100, various tests can to made to find the "best" that uses an integer multiply and a divide by power_of_2.
f(x) = x*a integer_divide power_of_2
For
f(x) = floor(x*log2(5)) = floor(x*some_float_c) the value of some_float_c is bounded by 100 minimum and maximums below.
x f(x) mn mx
f(x)/x (f(x) + 1)/x
1 2 2.00000 3.00000
2 4 2.00000 2.50000
3 6 2.00000 2.33333
...
59 136 2.30508 2.32203
...
87 202 2.32184 2.33333
...
98 227 2.31633 2.32653
99 229 2.31313 2.32323
100 232 2.32000 2.33000
The maximum min is 2.32184 and the minimum max is 2.32203, :
2.32184... <= some_float_c < 2.32203...
Since we cannot use float, find some_integer/some_power_of_2
2.32184... <= some_integer/some_power_of_2 < 2.32203...
ceil(some_power_of_2 * 2.32184...) <= some_integer < floor(some_power_of_2 * 2.32203...)
min max
2.32184 2.32203
2 5 4
4 10 9
8 19 18
...
1024 2378 2377
2048 4756 4755
4096 9511 9511 < first one where min <= max
8192 19021 19022
So 9511/4096 is the "simplest" and is a "best" candidate.
f(x) = (x*9511) integer_divide_by_power_of_2 4096
// In C
unsigned y = (x*9511u) >> 12;
Wikipedia
en.wikipedia.org › wiki › Logarithm
Logarithm - Wikipedia
2 weeks ago - The logarithm is denoted "logb x" (pronounced as "the logarithm of x to base b", "the base-b logarithm of x", or most commonly "the log, base b, of x"). An equivalent and more succinct definition is that the function logb is the inverse function to the function ... log10 150 is approximately 2.176, which lies between 2 and 3, just as 150 lies between 102 = 100 and 103 = 1000.
Cuemath
cuemath.com › algebra › log-base-2
Log Base 2 - Formula, Solution, Examples
Log base 2 is useful to write the exponential form with a base of 2 into logarithmic form. The number 20 = 1, 21 = 2, 22 = 4, 23 = 8, 24 = 16, but if we have 2x = 25 and we need to find the value of x, then we can first write it as log base 2 or \(log_225 = x\), and find the value of x.
Free Math Help Forum
freemathhelp.com › forums › free math help › beginning algebra
Logarithm question: I can't figure out how (log5)^2+(log2)^2+2log2log5 equals 1 | Free Math Help Forum
July 14, 2023 - ... You could solve the problem as follows: Let x=log5 and y = log2. Then the problem becomes x^2 + y^2 + 2xy = (x+y)^2 Now x+y = log 5 + log2 = log(5*2) = log 10 = 1. So, x^2 + y^2 + 2xy = (x+y)^2= (1)^2 = 1 ... Yes thanks. I’ve got it now. I appear to have started an interesting conversation.
Quora
quora.com › How-do-I-log-base-2-on-a-calculator
How to log base 2 on a calculator - Quora
If the calculator doesn’t have a key for logarithms with arbitrary bases, you use the change-of-base identity. For example: ... The latter works for any base; you just need to make sure you use the same base for both logs. Either use base-10 for both, or use natural logarithms for both. ... To calculate the logarithm base 2 on a calculator, you can use the "change of base" formula.
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List of log2 function values tables, log base 2 of numbers....Log base 2 Values Tables.log2(x) Notation Valuelog2(4) lb(4) 2log2(5) lb(5) 2.321928log2(6) lb(6) 2.584963log2(7) lb(7) 2.807355
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Step-by-step explanation:May be this is the incomplete question please send log 5 base 25 I will answer
Mathway
mathway.com › popular-problems › Algebra › 243780
Evaluate log base 2 of (2)^5 | Mathway
Evaluate log base 2 of (2)^5 · Step 1 · Use logarithm rules to move out of the exponent. Step 2 · Logarithm base of is . Step 3 · Multiply by . Please ensure that your password is at least 8 characters and contains each of the following: a number ·