Log Base 243 of 13

What is Log Base 243 of 13 or log243(13)?


Log243(13)

= 0.46694350389456

Formula How to

Share This Calculation:
Reference This Calculation:

How to find what is Log Base 243 of 13? 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 243 of 13 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log243(13) =
    loge(13)/loge(243)
  2. Calculate the log value for numerator and denominator part.
    2.5649493574615/5.4930614433405
  3. After simplify the fraction, you will get the result. Which is,
    0.46694350389456

log243(13) or Log Base 243 of 13 is equal to 0.46694350389456.

loge(243) 5.4930614433405
log10(243) 2.3856062735983

loge(13) 2.5649493574615
log10(13) 1.1139433523068

logb(x) Equal to
log243(8) 0.37855785214287
log243(9) 0.4
log243(10) 0.41918065485788
log243(11) 0.43653166772883
log243(12) 0.45237190142858
log243(13) 0.46694350389456
log243(14) 0.48043470054658
log243(15) 0.49299470414359
log243(16) 0.50474380285717
log243(17) 0.51578038463251
log243(18) 0.52618595071429