Evaluate \log_580

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Answered question

2021-11-06

Evaluate log580

Answer & Explanation

liannemdh

liannemdh

Skilled2021-11-07Added 106 answers

Step 1
The given expression is log580.
log580=log5(165)
Use the product rule of logarithms, logamn=logam+logbn  and  logamn=nlogam
log5(165)=log516+log55
=log542+log55
=2log54+log55
=2log522+1
=4log52+1
Step 2
Use the base change theorem, logab=lnblna
4log52+1=4ln2ln5+1
=40.4306+1
=1.7224+1
=2.7224

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