One question I know I completely bombed from my final today, anyone help me figure it out please?

Question

sleepyjess · Answer

It was 
Solve for x: $3^{x-2} = 6$

sleepyjess · Answer

I know I need to take the log of both sides, giving (x-2)log 3 = log 6, but was stuck after that

bmk614 · Answer

No. You actually just put the equation in logarithmic form. Which would be $$\log_{3}6=x-2 $$

bmk614 · Answer

You would then solve for x.

sleepyjess · Answer

How would I solve for x from that?

bmk614 · Answer

$$\log_{3}6+2=x $$

bmk614 · Answer

That should be your answer.

bmk614 · Answer

To get it simplified anymore, you would need to plug it into a calculator.

peachpi · Answer

you weren't wrong with what you did.

(x-2)log 3 = log 6

divide by log 3

x - 2 = (log 6)/(log 3)

add 2

x = 2 + (log 6)/(log 3)

which is the same as what @bmk614 got once you apply the change of base formula

sleepyjess · Answer

I was trying to distribute the x-2 and work from x log 3 - 2 log 3 = log 6, I see what I did wrong

peachpi · Answer

yeah, that's not wrong either.

 x log 3 - 2 log 3 = log 6

x log 3 = log 6 + 2 log 3

x = (log 6 + 2 log 3)/log 3

x = (log 6)/(log 3) + 2