Algebra 2
3^(x-5)=9

Could anyone please explain to me how to solve this?

a) x=-3
b)x=2
c)x=7
d)x=8

Question

Algebra 2
3^(x-5)=9

Could anyone please explain to me how to solve this?

a) x=-3
b)x=2
c)x=7
d)x=8

jim_thompson5910 · Answer

3^(x-5)=9

3^(x-5)=3^2

The bases are both equal to 3, so the exponents must be equal, which means

x-5 = 2

Solve for x to get your answer

anonymous · Answer

Oh! I forgot to break down 9 and I thought it was x-5=1 and that wasn't one of the choices. Thank you!

jim_thompson5910 · Answer

you're welcome

anonymous · Answer

That's a nice little trick if you're able to notice something like that.
The other thing you can do here is take log base 3 of both sides. You can think of log base 3 as being the opposite of 3^() so the operations will cancel out.

On the left side:
$$\Large \log_{3} (3^{x+5}) = x+5$$

On the right side:
$$\Large \log_{3}9 = 2 $$

And so you get x+5 = 2

anonymous · Answer

Thank you! I will keep that in mind if that ever shows up again. (: