Log Base 1002 of 3

What is Log Base 1002 of 3 or log1002(3)?

Log1002(3)

= 0.15899443060963

Formula How to
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Logarithm

How to find what is Log Base 1002 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 1002 of 3 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log1002(3) =
    loge(3)/loge(1002)
  2. Calculate the log value for numerator and denominator part.
    1.0986122886681/6.9097532816448
  3. After simplify the fraction, you will get the result. Which is,
    0.15899443060963

log1002(3) or Log Base 1002 of 3 is equal to 0.15899443060963.

loge(1002) 6.9097532816448
log10(1002) 3.0008677215312

loge(3) 1.0986122886681
log10(3) 0.47712125471966

logb(x) Equal to
log1002(1) 0
log1002(2) 0.10031431692377
log1002(3) 0.15899443060963
log1002(4) 0.20062863384753
log1002(5) 0.23292263078473
log1002(6) 0.25930874753339
log1002(7) 0.28161789136878
log1002(8) 0.3009429507713
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