Question

Solve 8^(x−5)=6 for x.

Answer 1

Take some kind of log of each side,\[\Large\rm \ln\left[8^{(x-5)}\right]=\ln(6)\]Do you remember your log rules? :)

Answer 2

\[\Large\rm \log(a^{\color{orangered}{b}})=\color{orangered}{b}\log(a)\]This one in particular.

Answer 3

It allows you to get the "x stuff" out of the exponent position,\[\Large\rm \ln\left[8^{\color{orangered}{(x-5)}}\right]=\ln(6)\]\[\Large\rm \color{orangered}{(x-5)} \ln[8]=\ln(6)\]

Answer 4

Shouldn't be too bad from there :O yah?
What do you think?

Answer 5

lol i got up to this part and got stuck

Answer 6

so you get x-5 = (ln6)/(ln8) right?

Answer 7

@zepdrix what should you do next?

Answer 8

Add......... 5? 0_o

Answer 9

\[\Large\rm x=\frac{\ln6}{\ln8}+5\]
Yah? :o
Weird place to get stuck :D lol

Answer 10

omg i didn't even notice that

Answer 11

lol thank you!!

Answer 12

np c:
If you're looking for a numerical value, you would have to rely on your calculator from this point on.