olve the logarithmic equations
$\log_3(x+1)=\log_4(x+8)$

The bases of this equation is different so
Let $\log_3(x+1)=y$...............................(i)
And
Let $\log_4(x+8)=y$...............................(ii)
By the laws of logarithm 
$3^y=x+1$...............................(iii)
$4^y=x+8$...............................(iv)
Solve eqn(iv) and (iii) simultaneously
$4^y-3^y=7$...............................(v)
Find all the possible values for which equation (v) is true.
The equation is true if $y=2$
$4^2-3^2=16-9=7$



You can check your solution by back substituting $y=2$ into equation (iii) and (iv).