What is 5log_{a}(x)+3log_{a}(y) ?

The solution to 5log_{a}(x)+3log_{a}(y) is log_{a}(x^5y^3)

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simplify 5log_{a}(x)+3log_{a}(y)

simplify

5 lo g_{a} (x) + 3 lo g_{a} (y)

lo g_{a} (x^{5} y^{3})

Solution steps

5 lo g_{a} (x) + 3 lo g_{a} (y)

Apply log rule:

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

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

= lo g_{a} (x^{5}) + 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^{5}) + lo g_{a} (y^{3})

Apply log rule:

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

lo g_{a} (x^{5}) + lo g_{a} (y^{3}) = lo g_{a} (x^{5} y^{3})

= lo g_{a} (x^{5} y^{3})

ln (\frac{1}{298}) \cdot 4.87

ln (\frac{118}{1})

ln (a \cdot e^{b \cdot x})

ln (6 x) + e^{x}

- 850 ln (\frac{50}{1500})

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