Question

solve for x. answer should not be approximation:
1+3ln(x-2)=13 and 2(5)^4x=7(5)^x
is there a way to put it into steps to make it easier to see how to set these up

Answer 1

1+3ln(x-2)=13
3ln(x-2)=12
ln(x-2)=4
e^(ln(x-2))=e^4
x-2=e^4
x=e^4-2

Answer 2

http://www.wolframalpha.com/input/?i=2%285%29^%284x%29%3D7%285%29^x

Answer 3

Do you have anything for the other part of the question? I know it's probably easy to solve but for some reason I can't seem to make it work for me, if you have anything I'd really appreciate it. Thanks

Answer 4

\[2(5)^{4x}=7(5)^x\implies5^{3x}=\frac72\]can you see what to do now?

Answer 5

I think I do
2(5)\[2(5)^{4x}\div(5)^{x} =7 \]\[2(5)^{x}\div2=7\div2\]\[5^{x}=\frac{ 7 }{ 2 }\]
Do these steps look right or am I just going about it the wrong way?