Solve the equation: 5^(2x+1) = 7, giving your answer correct to four decimal places.

First, we take logs of both sides: log(5^(2x+1))=log(7) Now, using the 3rd law of logs (index rule; using the power as the coefficient), we get: (2x+1)log(5)=log(7) i.e. 2x+1 = (log(7))/(log(5)) = 1.20906... Therefore, 2x=1.209...- 1 = 0.20906... i.e. x = 0.209.../2 = 0.10453... x = 0.1045 (c.t. 4d.p.)