Solve

3 log x = 1 + log (4x+5)/ log 2

3 log x = 1 + log (4x+5)/ log 2

That dividing logs stuff is quite unusual for introductory log problems. I will solve

3 log x = 1 + log (4x+5) - log 2
x^3 = 10*(4x+5)/2
2x^3-40x-50 = 0
2(x-5)(x^2+5x+5) = 0
and that's easy

If you really did mean to divide the logs, then I cannot find any real roots.