What is 2log_{10}(x)+3log_{10}(y) ?

The solution to 2log_{10}(x)+3log_{10}(y) is log_{10}(x^2y^3)

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simplify 2log_{10}(x)+3log_{10}(y)

simplify

2 lo g_{10} (x) + 3 lo g_{10} (y)

lo g_{10} (x^{2} y^{3})

Solution steps

2 lo g_{10} (x) + 3 lo g_{10} (y)

Apply log rule:

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

2 lo g_{10} (x) = lo g_{10} (x^{2})

= lo g_{10} (x^{2}) + 3 lo g_{10} (y)

Apply log rule:

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

3 lo g_{10} (y) = lo g_{10} (y^{3})

= lo g_{10} (x^{2}) + lo g_{10} (y^{3})

Apply log rule:

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

lo g_{10} (x^{2}) + lo g_{10} (y^{3}) = lo g_{10} (x^{2} y^{3})

= lo g_{10} (x^{2} y^{3})

lo g_{9} (9 x)

ln (k x)

lo g_{10} (y) + 3 lo g_{10} (z)

\frac{1}{3} lo g_{10} (x) + 3 lo g_{10} (x + 3)

ln (\frac{7}{2})

What is 2log_{10}(x)+3log_{10}(y) ?
The solution to 2log_{10}(x)+3log_{10}(y) is log_{10}(x^2y^3)