find v 2^v+8=3^2v-1

Question

Need help solving for v?

since the bases arent the same what would you do

Answer 1

2^v+8 = 3^2v-1

2^v•2⁸ = 3^2v•3^-1

256•2^v = (3²)^v /3 = 9^v/3

(9/2)^v = 256•3

v log(9/2) = log(256•3)

v = log(768)/log(4.5) = 4.417184