Log Base 5 of 65

What is Log Base 5 of 65 or log5(65)?

Log5(65)

= 2.5936926411671

Formula How to
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Logarithm

How to find what is Log Base 5 of 65? 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 5 of 65 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log5(65) =
    loge(65)/loge(5)
  2. Calculate the log value for numerator and denominator part.
    4.1743872698956/1.6094379124341
  3. After simplify the fraction, you will get the result. Which is,
    2.5936926411671

log5(65) or Log Base 5 of 65 is equal to 2.5936926411671.

loge(5) 1.6094379124341
log10(5) 0.69897000433602

loge(65) 4.1743872698956
log10(65) 1.8129133566429

logb(x) Equal to
log5(60) 2.5439593106328
log5(61) 2.5542295433789
log5(62) 2.5643327730507
log5(63) 2.5742743440941
log5(64) 2.5840593484404
log5(65) 2.5936926411671
log5(66) 2.6031788549644
log5(67) 2.6125224135126
log5(68) 2.6217275438694
log5(69) 2.6307982879524
log5(70) 2.6397385131956
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