Solve 7^(x - 2) = 12^x

Question

anonymous · Answer

Gotta use log...

anonymous · Answer

i know that much, but the thing is I got the answer, x = 3.28, and not the right answer of -7.22, if you could just give me the step by step process that would be great

anonymous · Answer

Okay:)

anonymous · Answer

ok so here's what I did, just instruct me on what i did wrong

anonymous · Answer

7^(x-2)=12^(x)

ln(7^(x-2))=ln(12^(x))

xln(7)-2ln(7)=ln(12^(x))

xln(7)-2ln(7)-xln(12)=0

x(ln(7)-ln(12))=2ln(7)

x=(2ln(7))/(ln(7)-ln(12))

x=3.8918

anonymous · Answer

$$(x-2)(\log(7)) =(x) \log(12) $$

anonymous · Answer

$$(x-2) (.8450984) = x(1.079181246)$$

anonymous · Answer

Uh hu...The sooner you turn it into a decimal the faster it gets farther from an exact answer. Just sayin. I think you did it correctly just rounding got the best of you!

anonymous · Answer

I"m not really rounding, I'm just putting out what the calc it putting out

anonymous · Answer

it's worked for all the other ones

anonymous · Answer

Well the calculator is rounding lol.

anonymous · Answer

yeah i guess the calc rounds

anonymous · Answer

lol

anonymous · Answer

Thanks though! I get it now

anonymous · Answer

Good:)