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Logarithmic functions are the inverse of exponential functions where the function is written as f(x) = log_{b} (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 log**_{x}32 = 5, find the value of the base ‘x’.

Given log_{x} 32 = 5

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

**log**_{b}(a) = N ** a = b**^{N}

**Hence log**_{x} 32 = 5 can be written as 32 = x^{5}

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

32 = 2^{5}

**32 = x**^{5 }** 2**^{5} = x^{5}

**Hence x = 2**

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

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

32 = 2

log_{3 }(x^{2}) = 4

**According to the formula, we have log (a**^{m}) = m * log a

Applying the above formula, we get

log_{3 }(x^{2}) = 4 2 * log_{3} (x) = 4

Dividing by ‘2’ on both sides log_{3} (x) = 4/2 log_{3} (x) = 2

**Now using the formula, log**_{b}(a) = N ** a = b**^{N}

We get, x = 3^{2}

x = 3 * 3

**x = 9**

Applying the above formula, we get

log

Dividing by ‘2’ on both sides log

We get, x = 3

x = 3 * 3