Solve.  Round answer to 2 decimal places.

7^(3x) = 8^(2x)

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have to solve 7^(3x) = 8^(2x)

Now the base of the two terms are not the same, so we use logarithms.

Take the logarithm of both the sides.

log( 7^(3x)) = log(8^(2x))

we use the relation log (a^b) = b*log a

=> 3x * log 7 = 2x * log 8

=> 3x * log 7 - 2x * log 8 = 0

=> x* (3 * log 7 - 2 * log 8) = 0

=> x = 0/ (3 * log 7 - 2 * log 8)

=> x = 0

Therefore the only possible value for x is x = 0

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial