Question

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

Answer 1

The answer is $x= \frac{log_{10} (243 )}{log_{10} (3 )}$

$3^{x} =243$
Logarithm both sides of the equation:
$log_{10} (3^{x} ) = log_{10} (243 )$
Since: $log (a^{b}) = b*log(a)$, then: $log_{10} (3^{x} ) =x*log_{10} (3 )$
Back to our equation:
$log_{10} (3^{x} ) = log_{10} (243 ) \\ x*log_{10} (3 ) = log_{10} (243 ) \\ x= \frac{log_{10} (243 )}{log_{10} (3 )}$