Log Base 4 of 216

What is Log Base 4 of 216 or log4(216)?


Log4(216)

= 3.8774437510817

Formula How to

Share This Calculation:
Reference This Calculation:

How to find what is Log Base 4 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 4 of 216 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log4(216) =
    loge(216)/loge(4)
  2. Calculate the log value for numerator and denominator part.
    5.3752784076842/1.3862943611199
  3. After simplify the fraction, you will get the result. Which is,
    3.8774437510817

log4(216) or Log Base 4 of 216 is equal to 3.8774437510817.

loge(4) 1.3862943611199
log10(4) 0.60205999132796

loge(216) 5.3752784076842
log10(216) 2.3344537511509

logb(x) Equal to
log4(211) 3.8605495943536
log4(212) 3.8639602272816
log4(213) 3.8673548101129
log4(214) 3.8707334932006
log4(215) 3.8740964247947
log4(216) 3.8774437510817
log4(217) 3.8807756162222
log4(218) 3.8840921623885
log4(219) 3.8873935298006
log4(220) 3.8906798567623
log4(221) 3.8939512796957