What is 5log_{3}(q)+2log_{3}(y) ?

The solution to 5log_{3}(q)+2log_{3}(y) is log_{3}(q^5y^2)

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simplify 5log_{3}(q)+2log_{3}(y)

simplify

5 lo g_{3} (q) + 2 lo g_{3} (y)

lo g_{3} (q^{5} y^{2})

Solution steps

5 lo g_{3} (q) + 2 lo g_{3} (y)

Apply log rule:

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

5 lo g_{3} (q) = lo g_{3} (q^{5})

= lo g_{3} (q^{5}) + 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} (q^{5}) + lo g_{3} (y^{2})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{3} (q^{5}) + lo g_{3} (y^{2}) = lo g_{3} (q^{5} y^{2})

= lo g_{3} (q^{5} y^{2})

ln (\frac{z}{x - y})

\frac{1}{3} ln (\frac{47}{56.37})

ln (3 e^{- 3 x})

\frac{2}{3} ln ((e^{2} + 1) (e + 1) (e - 1) (e^{8} + e^{4} + 1))

lo g_{\frac{35}{18}} (200) - lo g_{\frac{35}{18}} (4.1)

What is 5log_{3}(q)+2log_{3}(y) ?
The solution to 5log_{3}(q)+2log_{3}(y) is log_{3}(q^5y^2)