Log Base 8 of 64

What is Log Base 8 of 64 or log8(64)?

Log8(64)

= 2

Formula How to
Share This Calculation:
Reference This Calculation:
Logarithm

How to find what is Log Base 8 of 64? 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 8 of 64 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log8(64) =
    loge(64)/loge(8)
  2. Calculate the log value for numerator and denominator part.
    4.1588830833597/2.0794415416798
  3. After simplify the fraction, you will get the result. Which is,
    2

log8(64) or Log Base 8 of 64 is equal to 2.

loge(8) 2.0794415416798
log10(8) 0.90308998699194

loge(64) 4.1588830833597
log10(64) 1.8061799739839

logb(x) Equal to
log8(59) 1.9608810164539
log8(60) 1.9689635318695
log8(61) 1.9769124458543
log8(62) 1.9847321034623
log8(63) 1.9924266411666
log8(64) 2
log8(65) 2.0074559376762
log8(66) 2.0147980397862
log8(67) 2.0220297301526
log8(68) 2.0291542804168
log8(69) 2.0361748189261
Calculations