Question

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

Answer 1

Answer:

0.531 (3 s.f.)

Step-by-step explanation:

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

Power rule is used for the 3rd step.