Hey!
Okay, so if [tex]f(x)[/tex] equals [tex]g(x)[/tex], then [tex]In(f(x))[/tex] equals [tex]In(g(x))[/tex]. So, we'll plug in the numbers into this 'equation' we have now.
[tex]In(3^{x} ) = In(12 )[/tex]
And now we'll apply this log rule → [tex]log_{a} (x^{b} ) = b * log_{a} (x)[/tex]
[tex]In(3^{x} )=xIn(3) \\ xIn(3)=In(12)[/tex]
Now we have to solve [tex]In(3^{x} )=xIn(3) \\ xIn(3)=In(12)[/tex]. To do that, we'll divide both sides of the equation by [tex]In(3)[/tex].
[tex] \frac{xIn(3)}{In3} = \frac{In(12)}{In(3)} [/tex]
Now we simplify
[tex]x = \frac{In(12)}{In(3)}[/tex]
So, this means the equation [tex]3^{x} =12[/tex] solved is [tex]x = \frac{In(12)}{In(3)} [/tex] or 2.2619.
Hope this helps!
- Lindsey Frazier ♥
