Solve the exponential equation by converting to a common base:

Question

Show step by step work:

7^3x-1=7^-2x+14

Answer 1

Hello, Mona,

The expression given already has a common base, 7.

7^3x-1=7^-2x+14

Please correct this if a different expression was intended.

Assuming it is correct, since the bases are the same, we can say the exponents are equal to each other.

3x-1 = -2x + 14

5x = 15

x = 3

Check the result:

7^3x-1= 7⁸ = (5764801)

7^-2x+14 = 7⁸

I hope this helps,

Bob