log4x+log5(x-6)=2
Using Newton-Raphson method:
x ≈ 8.17927
\(x\approx 8.179270752839169853762493233675433392045\dots\)
\(x\approx 8.179\)
Here is a graphical solution
https://www.desmos.com/calculator/d0o5ls92qr