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

The solution to log_{10}(2x)+3log_{10}(2y) is log_{10}(16xy^3)

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

simplify

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

lo g_{10} (16 x y^{3})

Solution steps

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

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

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

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

Simplify

2 x (2 y)^{3} : 16 x y^{3}

= lo g_{10} (16 x y^{3})

lo g_{10} (p) - \frac{1}{3} lo g_{10} (q)

ln (5) + \frac{1}{2} ln (9)

lo g_{6} (\frac{x ^{3}}{y ^{8}})

ln (5) + \frac{1}{2} ln (4)

What is log_{10}(2x)+3log_{10}(2y) ?
The solution to log_{10}(2x)+3log_{10}(2y) is log_{10}(16xy^3)