How do you solve 9^(x-1)= 5^(2x)?

1 Answer
Mar 2, 2018

x=-2.150

Explanation:

Start by taking the logarithm of both sides, in order to bring the exponents down.

log_10(9^(x-1))=log_10(5^(2x))

One of the log rules is this:

log_a(x^n)=nlog_a(x)

So:

(x-1)log_10(9)=2xlog_10(5)

Evaluate the logarithm and simplify:

(x-1)(0.9542)=2x(0.6990)

0.9542x-0.9542=1.398x

-0.9542=0.4438x

x=-2.150