Log Base 4000 of 2

What is Log Base 4000 of 2 or log4000(2)?

Log4000(2)

= 0.083571621902111

Formula How to
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Logarithm

How to find what is Log Base 4000 of 2? 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 4000 of 2 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log4000(2) =
    loge(2)/loge(4000)
  2. Calculate the log value for numerator and denominator part.
    0.69314718055995/8.294049640102
  3. After simplify the fraction, you will get the result. Which is,
    0.083571621902111

log4000(2) or Log Base 4000 of 2 is equal to 0.083571621902111.

loge(4000) 8.294049640102
log10(4000) 3.602059991328

loge(2) 0.69314718055995
log10(2) 0.30102999566398

logb(x) Equal to
log4000(1) 0
log4000(2) 0.083571621902111
log4000(3) 0.13245788683929
log4000(4) 0.16714324380422
log4000(5) 0.19404729682982
log4000(6) 0.2160295087414
log4000(7) 0.23461520409123
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