Question

(75 POINTS PLEASE RESPOND ASAP)

Explain how to solve 4x + ^3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answer 1

Answer:

1.596

Step-by-step explanation:

So you can rewrite log as: $log_{b}a=x = > b^x=a$ So in this case it's already in exponential form which we'll use to rewrite into logarithm form.

$4^{x+3} = 7\\log_47=x+3\\\\\frac{log7}{log4}=x+3\\1.404\approx x+3\\x\approx1.596$

Answer 2

Answer:

x = -1.596

Explanation:

$\rightarrow \sf 4^{x + 3} = 7$

take log on both sides

$\rightarrow \sf log(4^{x + 3}) = log(7)$

$\rightarrow \sf (x + 3)log(4) = log(7)$

$\rightarrow \sf x + 3= \dfrac{log(7)}{log(4)}$

$\rightarrow \sf x= \dfrac{log(7)}{log(4)} -3$

calculate

$\rightarrow \sf x= -1.596322539$

$\rightarrow \sf x= -1.596 \quad (rounded \ to \ nearest \ thousand)$