Given :To solve for x we use the logarithm rule for powers.The log rule for powers states:We apply this rule to the left side of the equation.[tex] log_{5} x^{2} =log_{5} 4Both sides have log with same base so it can be eliminated.Eliminating log from both sides we have:[tex] x^{2} =4To solve for x we take root of both sides x=2,-2.