Question

Find the value of x

Answer 1

Answer:

$x = \dfrac{\log 26}{\log 8}$

$x \approx 1.567$

Step-by-step 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.

$\log 2^{3x + 1} = \log 52$

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

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

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

$3x \log 2 = \log 26$

$x = \dfrac{\log 26}{3 \log 2}$

$x = \dfrac{\log 26}{\log 2^3}$

$x = \dfrac{\log 26}{\log 8}$

$x \approx 1.567$