What is 4log_{3}(X)-2log_{3}(Y) ?

The solution to 4log_{3}(X)-2log_{3}(Y) is log_{3}((X^4)/(Y^2))

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simplify 4log_{3}(X)-2log_{3}(Y)

simplify

4 lo g_{3} (X) - 2 lo g_{3} (Y)

lo g_{3} (\frac{X ^{4}}{Y ^{2}})

Solution steps

4 lo g_{3} (X) - 2 lo g_{3} (Y)

Apply log rule:

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

4 lo g_{3} (X) = lo g_{3} (X^{4})

= lo g_{3} (X^{4}) - 2 lo g_{3} (Y)

Apply log rule:

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

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

= lo g_{3} (X^{4}) - lo g_{3} (Y^{2})

Apply log rule:

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

lo g_{3} (X^{4}) - lo g_{3} (Y^{2}) = lo g_{3} (\frac{X ^{4}}{Y ^{2}})

= lo g_{3} (\frac{X ^{4}}{Y ^{2}})

lo g_{10} (x^{3} - 7 x + 6) - lo g_{10} (x^{2} + x - 6)

ln (2 \cdot 5)

10 lo g_{10} (\frac{108}{10 8 _{0}})

3 ln (x^{2} y) - 2 ln (y)

\frac{d}{d x} (ln (x)) + ln (2 x)

What is 4log_{3}(X)-2log_{3}(Y) ?
The solution to 4log_{3}(X)-2log_{3}(Y) is log_{3}((X^4)/(Y^2))