What is expand log_{3}((x/(y^2))^2) ?

The solution to expand log_{3}((x/(y^2))^2) is 2(log_{3}(x)-2log_{3}(y))

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expand log_{3}((x/(y^2))^2)

expand

lo g_{3} ((\frac{x}{y ^{2}})^{2})

2 (lo g_{3} (x) - 2 lo g_{3} (y))

Solution steps

lo g_{3} ((\frac{x}{y ^{2}})^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{3} ((\frac{x}{y ^{2}})^{2}) = 2 lo g_{3} (\frac{x}{y ^{2}})

= 2 lo g_{3} (\frac{x}{y ^{2}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{3} (\frac{x}{y ^{2}}) = lo g_{3} (x) - lo g_{3} (y^{2})

= 2 (lo g_{3} (x) - lo g_{3} (y^{2}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{3} (y^{2}) = 2 lo g_{3} (y)

= 2 (lo g_{3} (x) - 2 lo g_{3} (y))

\frac{19.16}{0.0004 \cdot 60 \cdot 0.02} ln (\frac{1}{1 - 0.9})

ln (x^{2} + 1 + x^{4}) - ln (4 + 17)

\frac{1}{- 30} ln (\frac{7}{12})

100 + 20 \cdot ln (\frac{65}{65 - 38})

lo g_{10} (\frac{3}{u})

What is expand log_{3}((x/(y^2))^2) ?
The solution to expand log_{3}((x/(y^2))^2) is 2(log_{3}(x)-2log_{3}(y))