Log Base 27 of 9

What is Log Base 27 of 9 or log27(9)?


Log27(9)

= 0.66666666666667

Formula How to

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How to find what is Log Base 27 of 9? 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 27 of 9 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log27(9) =
    loge(9)/loge(27)
  2. Calculate the log value for numerator and denominator part.
    2.1972245773362/3.2958368660043
  3. After simplify the fraction, you will get the result. Which is,
    0.66666666666667

log27(9) or Log Base 27 of 9 is equal to 0.66666666666667.

loge(27) 3.2958368660043
log10(27) 1.431363764159

loge(9) 2.1972245773362
log10(9) 0.95424250943932

logb(x) Equal to
log27(4) 0.4206198357143
log27(5) 0.48832450690598
log27(6) 0.54364325119049
log27(7) 0.59041458305381
log27(8) 0.63092975357146
log27(9) 0.66666666666667
log27(10) 0.69863442476313
log27(11) 0.72755277954805
log27(12) 0.75395316904764
log27(13) 0.7782391731576
log27(14) 0.80072450091096