Question

Solve for b

8 to the power of b-1=2 to the power of 4b+4 or if it is easier for you to understand this way 8^b-1=2^4b+4

Answer 1

I'm just here to confirm that -7 is the right answer.

Answer 2

b = - 7

Explanation:

note that 8 = 2³, hence

( 2³)^(b - 1) =
`2^(4b+4)`

since the bases on both sides of the equation are 2, equate the exponents

4b + 4 = 3b - 3 ( subtract 3b from both sides )

b + 4 = - 3 ( subtract 4 from both sides )

b = - 7