Question 734300
Base is "a", so ignoring this in the notation,

First trick is dealing with the negative sign on the right.
{{{log((x+sqrt(x^2-5))/5)=log(1/(x-sqrt(x^2-5)))}}}


Take logarithms of left side and right side.
{{{(x+sqrt(x^2-5))/5=1/(x-sqrt(x^2-5))}}}


Next important trick (technique) is multiply numerator and denominator on the right side by the conjugate of the denominator.
{{{(x+sqrt(x^2-5))/5=(1/(x-sqrt(x^2-5)))*((x+sqrt(x^2-5))/(x+sqrt(x^2-5)))}}}
{{{(x+sqrt(x^2-5))/5=(x+sqrt(x^2-5))/(x^2-x^2+5)}}}
{{{(x+sqrt(x^2-5))/5=(x+sqrt(x^2-5))/5}}}
DONE.