Question

Log question: How do I solve for x? 9^4x+5 = 6^2x+8

Answer 1

\[9^{4x+5}=6^{2x+8}\]

Answer 2

and then I get (4x+5)log9=(2x+8)log6

Answer 3

but I don't know how to simplify that any further

Answer 4

well distribute and you get

4xlog(9) + 5log(9) = 2xlog(6) + 8 log(6)

collect like terms

4xlog(9) - 2xlog(6) = 8log(6) - 5log(9)

which is

x(4log(9) - 2log(6)) = 8log(6) - 5log(9)

hopefully this helps... do you need an exact value or just an answer to 3 or so decimal places

Answer 5

I just need to have x equal a simplified fraction so it would be x= 8log6-5log9/4log9-2log6

Answer 6

thanks for your help!

Answer 7

thats basically the answer, but it can be simplified by applying log laws for powers and subtraction..