Question

How do you solve `(16+ \frac { 878} { 26} ) ^ { 3t } = 2`?

Answer 1

`t=0.059131198`

Explanation:

`(16+878/26)^(3t)=2`

1) Using the law `lnm^n=nlnm`, take the natural log (ln) of both sides of the equation to prevent the variable from being an exponent.
`ln(16+878/26)^(3t)=ln(2)`
`(3t)ln(16+878/26)=ln(2)`

2) Isolate `t`.
`(3t)=ln(2)/ln(16+878/26)`
`t=ln(2)/ln(16+878/26)*1/3`

3) Solve using a calculator.
`t=0.059131198`