What are the steps to solve an equation with logarithms on both sides?

[kalistella]

Hi

I need some help!

Doing A'level logarithms and am stuck.

log3(x-1)=log8(x+1)

So far, I have done these steps...
(x-1)log3=(x+1)log8
xlog3-log3=xlog8+log8
xlog3-xlog8-log3-log8

Not sure what to do next to get the solution for x. Everything I do gets the wrong answer. I need an explanation in simple terms!

Any help greatly appreciated!

 

[HallsofIvy]

Hi

I need some help!

Doing A'level logarithms and am stuck.

log3(x-1)=log8(x+1)

Do you mean log(3(x-1)), log₃(x-1) or log 3^x-1?
(If you can't do subscripts or superscripts, use log_3(x-1) or log 3^(x-1).)

So far, I have done these steps...
(x-1)log3=(x+1)log8

Okay, it must be log(3^x-1)= log(8^x+1)

xlog3-log3=xlog8+log8
xlog3-xlog8-log3-log8

Whoops, what happened to the "="?? I assume you meant
xlog(3)- xlog(8)= log(8)- log(3)

Not sure what to do next to get the solution for x. Everything I do gets the wrong answer. I need an explanation in simple terms!

Any help greatly appreciated!

xlog(3)- xlog(8)= log(8)- log(3)
x(log(3)- log(8))= log(8)- log(3)
x= (log(8)- log(3))/(log(3)- log(8))