Answer:
[tex] x = \dfrac{\log 26}{\log 8} [/tex]
[tex] x \approx 1.567 [/tex]
Step-by-step explanation:
The angles whose measures are shown are supplementary.
[tex] 2^{3x + 1} = 52 [/tex]
Since you have a variable in an exponent, you must use logarithms to solve the equation.
[tex] \log 2^{3x + 1} = \log 52 [/tex]
[tex] (3x + 1) \log 2 = \log 52 [/tex]
[tex] 3x \log 2 + \log 2 = \log 52 [/tex]
[tex] 3x \log 2 = \log 52 - \log 2 [/tex]
[tex] 3x \log 2 = \log 26 [/tex]
[tex] x = \dfrac{\log 26}{3 \log 2} [/tex]
[tex] x = \dfrac{\log 26}{\log 2^3} [/tex]
[tex] x = \dfrac{\log 26}{\log 8} [/tex]
[tex] x \approx 1.567 [/tex]
