Solve for the following exponential equations. Use the natural logarithm in your

Dottie Parra

Dottie Parra

Answered question

2021-09-23

Solve for the following exponential equations. Use the natural logarithm in your answer(where applicable) for full credit. Use rules for exponents, factor and simplify.
41x=32x+5

Answer & Explanation

Aamina Herring

Aamina Herring

Skilled2021-09-24Added 85 answers

We have,
41x=32x+5
Taking logarithm on both of the side and solving further, we get result as
(1x)log4=(2x+5)log3
log4(log4)x=(2log3)x+5log3
Taking the term related x on one of the side,
(log45log3)=(2log3+log4)x
log4log35=(log32+log4)x
x=(log4log243)(log9+log4)
Using the logarithm property logmlogn=log(mn) and logm+logn=log(mn) and solving further, we get the result as
x=(log4log243)(log9+log4)
x=log(4243)log36
x=log36(4243)
Hence, value of x will be x=log364243,

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