# Given the exponential equation 2^{x} = 8, what is the logarithmic form of the equation in base 10?

**Solution:**

It is given that,

Exponential equation 2^{x} = 8.

We have to find the logarithmic form of the equation in base 10.

By the change base rule (inverse of exponential function)

a^{b} = c is equal to log_{a}(c) = b

So, 2^{x} = 8 in to logarithm from log_{2}(8) = x

Then into the base 10 logarithmic form.

By the change of base formula

log_{b}(a) = log_{10}(a)/log_{10}(b)

Then, log_{2}(8) = log_{10}(8)/log_{10}(2)

Therefore, the logarithmic form of the equation in base 10 is log_{10}(8)/log_{10}(2)

## Given the exponential equation 2^{x} = 8, what is the logarithmic form of the equation in base 10?

**Summary:**

Given the exponential equation 2^{x} = 8, the logarithmic form of the equation in base 10 is log_{10}(8)/log_{10}(2).

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