Write the expression as one logarithm . SNIPP \log(x^3y^2)-2\log x\sqrt[3

Trent Carpenter

Trent Carpenter

Answered question

2021-11-06

Write the expression as one logarithm . SNIPP
log(x3y2)2logx3{y}3log(xy)

Answer & Explanation

unett

unett

Skilled2021-11-07Added 119 answers

Step 1
Given that:
log(x3y2)2logx3{y}3log(xy)
Step 2
To write the given expression in one logarithms,
Apply   division   rules: log(a)log(b)=log(ab) and 
alog(b)=log(b)a
So,
\(\displaystyle{\log{{\left({x}^{{3}}{y}^{{2}}\right)}}}−{2}{\log{{\left({x}\sqrt{{{3}}}{\left\lbrace{y}\right\rbrace}\right)}}}−{3}{\log{{\left({\frac{{{x}}}{{{y}}}}\right)}}}={\log{{\left({x}^{{3}}{y}^{{2}}\right)}}}−{{\log{{\left({x}\sqrt{{{3}}}{y}\right)}}}^{{2}}

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