# Given the exponential equation 3^{x} = 243, what is the logarithmic form of the equation in base 10?

**Solution:**

The given exponential equation is 3^{x} = 243

Take logarithm on both sides

log_{10 }(3^{x}) = log_{10 }(243) ------->(1)

We know that

log (a^{b}) = b × log (a)

So we get

log_{10} (3^{x}) = x ×log_{10} (3)----------->2)

Substitute (2) in (1)

Thus log_{10} (3^{x}) = log_{10} (243)

⇒ x ×log_{10} (3) = log_{10} (243)

x =log_{10} (243)/ log_{10}(3)

Therefore, the logarithmic form of the equation in base 10 is x = log_{10}(243)/ log_{10} (3).

## Given the exponential equation 3^{x} = 243, what is the logarithmic form of the equation in base 10?

**Summary:**

Given the exponential equation 3^{x} = 243, the logarithmic form of the equation in base 10 is x =log_{10 }(243)/ log10 (3).