Question

What is the solution of the equation 3^x=12? Round your answer to the nearest ten-thousandth.

Answer 1

Hey!


Okay, so if  $f(x)$  equals  $g(x)$,  then $In(f(x))$  equals  $In(g(x))$.  So, we'll plug in the numbers into this 'equation' we have now.

$In(3^{x} ) = In(12 )$

And now we'll apply this log rule →  $log_{a} (x^{b} ) = b * log_{a} (x)$

$In(3^{x} )=xIn(3) \\ xIn(3)=In(12)$

Now we have to solve $In(3^{x} )=xIn(3) \\ xIn(3)=In(12)$. To do that, we'll divide both sides of the equation by  $In(3)$.

$\frac{xIn(3)}{In3} = \frac{In(12)}{In(3)}$

Now we simplify

$x = \frac{In(12)}{In(3)}$

So, this means the equation  $3^{x} =12$  solved is  $x = \frac{In(12)}{In(3)}$  or  2.2619.

Hope this helps!


- Lindsey Frazier ♥

Answer 2

The answer is D.) 2.2619.