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

x = -1.596

Step-by-step 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= (log(7))/(log(4))`

`\rightarrow \sf x= (log(7))/(log(4)) -3`

calculate

`\rightarrow \sf x= -1.596322539`

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

Answer 2

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\\\\(log7)/(log4)=x+3\\1.404\approx x+3\\x\approx1.596`