Question

Solve the equation: 5^(3t)=13

Answer 1

0.531 (3 s.f.)

Explanation:

`{5}^(3t) = 13 \\ lg {5}^(3t) = lg13 \: \: \: \: (log \: both \: sides) \\ 3t(lg5) = lg13 \\ 3t = (lg13)/(lg5) \\ t = (1)/(3) ( (lg13)/(lg5) ) \\ t = (lg13)/(3lg5) \\ t = 0.531 \: (3 \: s.f.)`

Power rule is used for the 3rd step.