Question

Mike is working on solving the exponential equation 37x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.

Use the change of base formula: log base b of y equals log y over log b.

Answer 1

$~~~~~37^x = 12\\\\\implies \ln\left( 37^x \right) = \ln(12)\\\\\implies x \ln (37) = \ln(12)\\\\\implies x = \dfrac{\ln(12)}{\ln(37)}\\\\\implies x \approx 0.689$