Normally, I discourage students from changing to base x because it takes more steps to solve for x as we subsequently have to remove x as the base. However we need to be flexible in thought. If you look at the above logarithm, you realize that if you change the base to x, you can manipulate and simplify the equation quickly, you can then remove base x by moving the x across the equal sign (see third last line of the solution).
Additional Math (amath) Tuition 1 to 1 or pair Tuition at Woodlands. Yew Tee, Choa Chu Kang, Yishun & Sembawang.