Log Base 42 of 5

What is Log Base 42 of 5 or log42(5)?

Log42(5)

= 0.43059929763757

Formula How to
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Logarithm

How to find what is Log Base 42 of 5? 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 42 of 5 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log42(5) =
    loge(5)/loge(42)
  2. Calculate the log value for numerator and denominator part.
    1.6094379124341/3.7376696182834
  3. After simplify the fraction, you will get the result. Which is,
    0.43059929763757

log42(5) or Log Base 42 of 5 is equal to 0.43059929763757.

loge(42) 3.7376696182834
log10(42) 1.6232492903979

loge(5) 1.6094379124341
log10(5) 0.69897000433602

logb(x) Equal to
log42(1) 0
log42(2) 0.18544902341537
log42(3) 0.29392974790872
log42(4) 0.37089804683074
log42(5) 0.43059929763757
log42(6) 0.47937877132409
log42(7) 0.52062122867591
log42(8) 0.55634707024611
log42(9) 0.58785949581744
log42(10) 0.61604832105294
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