Log Base 3 of 81

What is Log Base 3 of 81 or log3(81)?

Log3(81)

= 4

Formula How to
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Logarithm

How to find what is Log Base 3 of 81? 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 3 of 81 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log3(81) =
    loge(81)/loge(3)
  2. Calculate the log value for numerator and denominator part.
    4.3944491546724/1.0986122886681
  3. After simplify the fraction, you will get the result. Which is,
    4

logb(x) Equal to
log3(76) 3.9420033663893
log3(77) 3.9539020878056
log3(78) 3.9656472730442
log3(79) 3.9772428340159
log3(80) 3.9886925350038
log3(81) 4
log3(82) 4.0111687195914
log3(83) 4.022202057428
log3(84) 4.0331032563043
log3(85) 4.0438754438805
log3(86) 4.0545216380691

log3(81) or Log Base 3 of 81 is equal to 4.

loge(3) 1.0986122886681
log10(3) 0.47712125471966

loge(81) 4.3944491546724
log10(81) 1.9084850188786
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