If \log_a(x)=1.5 and \log_a(y)=4.7 find the following u

Efan Halliday 2021-11-05 Answered
If
\(\displaystyle{{\log}_{{a}}{\left({x}\right)}}={1.5}\)
and \(\displaystyle{{\log}_{{a}}{\left({y}\right)}}={4.7}\)
find the following using the properties of logarithms.
\(\displaystyle{{\log}_{{a}}{\left({\frac{{{x}}}{{{y}}}}\right)}}\)

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Expert Answer

Alara Mccarthy
Answered 2021-11-06 Author has 13949 answers
Step 1
properties of logarithms
\(\displaystyle{{\log}_{{a}}{\left({\frac{{{x}}}{{{y}}}}\right)}}={\frac{{{{\log}_{{a}}{\left({x}\right)}}}}{{{{\log}_{{a}}{\left({y}\right)}}}}}\)
Now
\(\displaystyle{{\log}_{{a}}{\left({x}\right)}}={1.5}\)
\(\displaystyle{{\log}_{{a}}{\left({y}\right)}}={4.7}\)
Step 2
from property
\(\displaystyle{{\log}_{{a}}{\left({\frac{{{x}}}{{{y}}}}\right)}}\)
\(\displaystyle={\frac{{{{\log}_{{a}}{\left({x}\right)}}}}{{{{\log}_{{a}}{\left({y}\right)}}}}}\)
\(\displaystyle={\frac{{{1.5}}}{{{4.7}}}}\)
=0.3191
\(\displaystyle{{\log}_{{a}}{\left({\frac{{{x}}}{{{y}}}}\right)}}={0.3191}\) Answer
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