6^7x-5 = 8^4x-2

Question

I couldn't figure it out! Please help!

Answer 1

6^7x-5 = 8^4x-2

Using any base > 1, take the logarithm of both sides:

(7x-5)*log(6) = (4x-2)*log(8)

Distribute and re-arrange:

7x log 6 - 4x log 8 = -2 log 8 + 5 log 6

Factor out x and solve:

x = ( -2 log 8 + 5 log 6 ) / ( 7 log 6 - 4 log 8 )

= 1.1362, ans