Log Base 6 of 216

What is Log Base 6 of 216 or log6(216)?

Log6(216)

= 3

Formula How to
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Logarithm

How to find what is Log Base 6 of 216? 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 6 of 216 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log6(216) =
    loge(216)/loge(6)
  2. Calculate the log value for numerator and denominator part.
    5.3752784076842/1.7917594692281
  3. After simplify the fraction, you will get the result. Which is,
    3

log6(216) or Log Base 6 of 216 is equal to 3.

loge(6) 1.7917594692281
log10(6) 0.77815125038364

loge(216) 5.3752784076842
log10(216) 2.3344537511509

logb(x) Equal to
log6(211) 2.9869288960877
log6(212) 2.989567721933
log6(213) 2.9921941297284
log6(214) 2.9948082358028
log6(215) 2.9974101548583
log6(216) 3
log6(217) 3.0025778827659
log6(218) 3.0051439131553
log6(219) 3.0076981996575
log6(220) 3.0102408492788
log6(221) 3.0127719675696
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