Question

Find the value of x

It would be really helpful if you could explain what to do with the 2^3x+1

Answer 1

`x = (\log 26)/(\log 8)`

`x \approx 1.567`

Explanation:

The angles whose measures are shown are supplementary.

`2^(3x + 1) = 52`

Since you have a variable in an exponent, you must use logarithms to solve the equation.

`\log 2^(3x + 1) = \log 52`

`(3x + 1) \log 2 = \log 52`

`3x \log 2 + \log 2 = \log 52`

`3x \log 2 = \log 52 - \log 2`

`3x \log 2 = \log 26`

`x = (\log 26)/(3 \log 2)`

`x = (\log 26)/(\log 2^3)`

`x = (\log 26)/(\log 8)`

`x \approx 1.567`