Condense the following log expression.-2\log_3(xy)+\frac{4}{5}\log_3z^{1

Suman Cole 2021-10-20 Answered

Condense the following log expression.
2log3(xy)+45log3z10+log3(x+1)

xlogab=logabx

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Expert Answer

averes8
Answered 2021-10-21 Author has 92 answers

Step 1
Condensing the logarithmic expression.
Given:
2log3(xy)+45log3z10+log3(x+1)

xlogab=logabx
Apply log rule: xlogab=logabx
log3(xy)2+log3(z10)45+log3(x+1)
Step 2
By the property of logarithms.
loga(cd)=logac+logad
log3(xy)2+log3(z8)+log3(x+1)
log3(xy)2+log3(z8(x+1))
Step 3
By the property of logarithms.
loga(cd)=logaclogad
log3(z8(x+1))log3(xy)2
log3(z8(x+1)(xy)2)

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