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

Asked by maham237 @ 17/12/2020 in Mathematics viewed by 310 People

Answered by maham237 @ 17/12/2020

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:
$log_{10} (3^{x} ) = log_{10} (243 ) \\ 
x*log_{10} (3 ) = log_{10} (243 ) \\ 
x= \frac{log_{10} (243 )}{log_{10} (3 )}$

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