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(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.

(75 POINTS PLEASE RESPOND ASAP) Explain how to solve 4x + ^3 = 7 using the change-example-1
User Rivenfall
by
2.5k points

2 Answers

15 votes
15 votes

Answer:

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)

User Dennan Hogue
by
3.3k points
15 votes
15 votes

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

User Doug Ayers
by
3.1k points
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