What is 2log_{a}(x)-3log_{a}(y) ?

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

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simplify 2log_{a}(x)-3log_{a}(y)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 lo g_{a} (x) = lo g_{a} (x^{2})

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

3 lo g_{c} (y) - \frac{15}{4} lo g_{c} (x)

\frac{1}{3} (6 ln (x + 5) + ln (x) - ln (x^{2} - 6))

1.464 - lo g_{10} (\frac{1}{1 0 ^{0.3}})

\frac{( ln ( 2 ) \cdot 45 )}{ln ( 10 ) - ln ( 2 )}

- 20 lo g_{10} (0.2 1 - 0.01)

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