Question

Please help solving the following logarithm: 8^(x-9) = 19^(3x+2)

Answer 1

So far, I have log8^(x-9) = log19^(3x+2)
(x-9)log8 = (3x+2)log19

Answer 2

so far so good. :)

Next step = distribute log(8) over (x-9) and distribute log(19) to (3x+2).

Answer 3

ok...got that...xlog8-9log8 = 3xlog19 + 2log19

Answer 4

i always miss it at this step.

Answer 5

Hint -- it's best to put parenthesis around log(number). log is a function, and the number is the input or independent variable. :)

Ok, so the next step here is to "get all the xs on one side" and "get all the log(number) on the other."

Answer 6

(3xlog19-xlog8) = (9log8-2log19) ???

Answer 7

Yes. Only thing, use parenthesis around the log of the number...

(3xlog(19)-xlog(8)) = (9log(8)-2log(19))
instead of
(3xlog19-xlog8) = (9log8-2log19)

This is because log(19), log(8) -- pronounced "Log of 19", "log of 8" etc... are numbers. So they are just the same as... if you like, 2 or 3. In the sense they are numbers or constants.

Ok, next step -- factor out the x from the expression on the left.

(3xlog(19)-xlog(8)) = ?? (factor out the x)

Answer 8

x(3log(19) - log(8))

Answer 9

Yup!

Now that is still equal to (9log(8)-2log(19))

So you now have

x(3log(19) - log(8)) = (9log(8)-2log(19))

It's important to keep in mind that 3log(19) is just a number, as is log(8). So their difference is just a number, it's sort of like saying...

x*4 = (9log(8)-2log(19))

What would you do next?

Answer 10

diviide

Answer 11

Yup. :) The final answer will be a big fraction with logs in the numerator and denominator.

Answer 12

i divided 9log(8)-2log(19) on both sides, is that correct

Answer 13

i'm confusing myslef all over again

Answer 14

is the answer x=2log(19)+9log(8)/3log(19)-log8

Answer 15

are you still there?

Answer 16

thank you