Evaluate log <mrow class="MJX-TeXAtom-ORD"> 5 </mrow> </msub> &#x20

Bailee Landry

Bailee Landry

Answered question

2022-05-21

Evaluate log 5 19 2 / ( log 3 15 )
I did this, but I get 1.484, whereas it's 1.038 in my book.
I used the method:
log a b = log c b log c a

Answer & Explanation

Bruce Bridges

Bruce Bridges

Beginner2022-05-22Added 13 answers

Using the law of logarithms:
log n ( x a ) a log n ( x )
We have your expression:
2 log 5 ( 19 ) log 3 ( 15 )
Writing these in terms of the natural logarithm ln ( ), we have (using a calculator or tables):
2 ln ( 19 ) ln ( 5 ) × ln ( 3 ) ln ( 15 ) 1.4843
So your book does appear to be wrong.

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