What is 5log_{b}(x)+6log_{b}(y) ?

The solution to 5log_{b}(x)+6log_{b}(y) is log_{b}(x^5y^6)

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simplify 5log_{b}(x)+6log_{b}(y)

simplify

5 lo g_{b} (x) + 6 lo g_{b} (y)

lo g_{b} (x^{5} y^{6})

Solution steps

5 lo g_{b} (x) + 6 lo g_{b} (y)

Apply log rule:

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

5 lo g_{b} (x) = lo g_{b} (x^{5})

= lo g_{b} (x^{5}) + 6 lo g_{b} (y)

Apply log rule:

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

6 lo g_{b} (y) = lo g_{b} (y^{6})

= lo g_{b} (x^{5}) + lo g_{b} (y^{6})

Apply log rule:

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

lo g_{b} (x^{5}) + lo g_{b} (y^{6}) = lo g_{b} (x^{5} y^{6})

= lo g_{b} (x^{5} y^{6})

\frac{1}{5} (lo g_{3} (x) + lo g_{3} (x - 2))

lo g_{10} (5) + lo g_{10} (3)

lo g_{b} (\frac{x ^{3} y}{z ^{8}})

ln (x) + ln (2)

lo g_{5} (10 x)

What is 5log_{b}(x)+6log_{b}(y) ?
The solution to 5log_{b}(x)+6log_{b}(y) is log_{b}(x^5y^6)