Log Base 240 of 3

What is Log Base 240 of 3 or log240(3)?

Log240(3)

= 0.20045332378842

Formula How to
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Logarithm

How to find what is Log Base 240 of 3? 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 240 of 3 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log240(3) =
    loge(3)/loge(240)
  2. Calculate the log value for numerator and denominator part.
    1.0986122886681/5.480638923342
  3. After simplify the fraction, you will get the result. Which is,
    0.20045332378842

log240(3) or Log Base 240 of 3 is equal to 0.20045332378842.

loge(240) 5.480638923342
log10(240) 2.3802112417116

loge(3) 1.0986122886681
log10(3) 0.47712125471966

logb(x) Equal to
log240(1) 0
log240(2) 0.12647196618041
log240(3) 0.20045332378842
log240(4) 0.25294393236082
log240(5) 0.29365881148994
log240(6) 0.32692528996883
log240(7) 0.35505169675888
log240(8) 0.37941589854123
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