Log Base 64 of 8

What is Log Base 64 of 8 or log64(8)?

Log64(8)

= 0.5

Formula How to
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Logarithm

How to find what is Log Base 64 of 8? The logarithm of a number to a given base is the exponent to which the base must be raised to produce the number. In mathematical terms, if "b" is the base and "x" is the number, then the logarithm of "x" to the base "b" is written as logb(x) and is defined as the exponent "y" such that b^y = x.

The logarithm of a number to a given base is a useful tool in many areas of mathematics and science, including finance, engineering, and physics. It's also used in solving exponential equations and in graphing logarithmic functions.

In mathematics, the most common logarithms are logarithms to the base 10, which are called common logarithms, and logarithms to the base e, which are called natural logarithms. The natural logarithm is denoted by the symbol ln, and has special properties in calculus and other areas of mathematics.

To calculate any "log base of" use this fromula, which is given below-

logb(x) =
loge(x)/loge(b)
; x>0, b>1;

Where,

  • b = base;
  • x = value;

For calculation, here's how to calculate log base 64 of 8 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log64(8) =
    loge(8)/loge(64)
  2. Calculate the log value for numerator and denominator part.
    2.0794415416798/4.1588830833597
  3. After simplify the fraction, you will get the result. Which is,
    0.5

log64(8) or Log Base 64 of 8 is equal to 0.5.

loge(64) 4.1588830833597
log10(64) 1.8061799739839

loge(8) 2.0794415416798
log10(8) 0.90308998699194

logb(x) Equal to
log64(3) 0.26416041678686
log64(4) 0.33333333333333
log64(5) 0.38698801581456
log64(6) 0.43082708345353
log64(7) 0.4678924870096
log64(8) 0.5
log64(9) 0.52832083357372
log64(10) 0.55365468248123
log64(11) 0.57657193643955
log64(12) 0.59749375012019
log64(13) 0.61673995302352
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