Evaluate log3/8 91 using the change of base formula. Round your answer to one decimal place.

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03-11-2022
Mathematics

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Evaluate log3/8 91 using the change of base formula. Round your answer to one decimal place.

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TrevanG419400 TrevanG419400 · Answer 1 · 2022-11-03T14:28:19-04:00

TrevanG419400 TrevanG419400

03-11-2022

We have to apply the change of base formula:

[tex]\log _b(a)=\frac{\log _x(a)}{\log _x(b)}[/tex]

We can apply this to our expression as:

[tex]\log _{\frac{3}{8}}(91)=\frac{\ln(91)}{\ln(\frac{3}{8})}=\frac{\ln (91)}{\ln (3)-\ln (8)}\approx\frac{4.511}{1.099-2.079}=\frac{4.511}{-0.980}\approx-4.6[/tex]

Answer: -4.6

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