Question 600332
{{{log(4,(x+1))-log(4,(x)) = 3}}} Start with the given equation


{{{log(4,((x+1)/x)) = 3}}} Condense the logs using the identity {{{log(b,(X)) - log(b,(Y)) = log(b,(X/Y))}}}


{{{(x+1)/x = 4^3}}} Convert to exponential form.


{{{(x+1)/x = 64}}} Cube 4 to get 64


{{{x+1 = 64x}}} Multiply both sides by x


{{{1 = 64x-x}}} Subtract x from both sides


{{{1 = 63x}}} Combine like terms


{{{1/63 = x}}} Divide both sides by 63 to isolate x


{{{x = 1/63}}} Flip the equation.



So the solution is {{{x = 1/63}}}