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Log Calculator - Online Calculator - Tutorpace

# Log Calculator

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Logarithmic functions are the inverse of exponential functions where the function is written as f(x) = logb (a) such that ‘b’ >0, b = 1 and a> 0. This is read as “log base b of a”. Log calculator is the tool which can simplify or compute the logarithm values of different numbers.

Example 1: Given logx32 = 5, find the value of the base ‘x’.
Given logx 32 = 5

Convert this Logarithmic equation to Exponential equation by using the formula,

logb(a) = N   a = bN

Hence logx 32 = 5 can be written as 32 = x5

Now we prime factorization of 32 = 2 * 2 * 2 * 2 * 2

32 = 25

32 = x 25 = x5

Hence x = 2

Example 2: Given log3 (x2) = 4, then solve for ‘x’.
log3 (x2) = 4
According to the formula, we have log (am) = m * log a

Applying the above formula, we get

log3 (x2) = 4   2 * log3 (x) = 4

Dividing by ‘2’ on both sides  log3 (x) = 4/2  log3 (x) = 2

Now using the formula, logb(a) = N   a = bN

We get, x = 32

x = 3 * 3

x = 9