Question

Solve the equation. Round to the nearest hundredth. Show work.


`2.8` ·
`13^(4x) +4.8 = 19.3`

Answer 1

Final answer is approx x=0.16.

Explanation:

Given equation is
`2.8* 13^(4x) +4.8 = 19.3`

Now we need to solve equation
`2.8* 13^(4x) +4.8 = 19.3` and round to the nearest hundredth.

`2.8* 13^(4x) +4.8 = 19.3`

`2.8* 13^(4x) = 19.3-4.8`

`2.8* 13^(4x) = 14.5`

`13^(4x) = (14.5)/(2.8)`

`13^(4x) = 5.17857142857`

`\log(13^(4x)) = \log(5.17857142857)`

`4x \log(13) = \log(5.17857142857)`

`4x = (\log(5.17857142857))/(\log\left(13\right))`

`4x = 0.641154659628`

`x = (0.641154659628)/(4)`

`x = 0.160288664907`

Round to the nearest hundredth.

Hence final answer is approx x=0.16.