What is 5log_{10}(x)+3log_{10}(y) ?

The solution to 5log_{10}(x)+3log_{10}(y) is log_{10}(x^5y^3)

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simplify 5log_{10}(x)+3log_{10}(y)

simplify

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

lo g_{10} (x^{5} y^{3})

Solution steps

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

Apply log rule:

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

5 lo g_{10} (x) = lo g_{10} (x^{5})

= lo g_{10} (x^{5}) + 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^{5}) + lo g_{10} (y^{3})

Apply log rule:

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

lo g_{10} (x^{5}) + lo g_{10} (y^{3}) = lo g_{10} (x^{5} y^{3})

= lo g_{10} (x^{5} y^{3})

lo g_{3} (x) + 4 lo g_{3} (y)

\frac{1}{3} ln ∣ y - 1 ∣ - \frac{1}{3} ln ∣ y + 2 ∣

ln (20) + 2 ln (\frac{1}{2}) + \frac{1}{3} ln (27)

3.3 ln (6) - 7.2 ln (2) - 0.9 ln (2)

ln (\frac{e ^{x} + 2}{e ^{x} - 2})

What is 5log_{10}(x)+3log_{10}(y) ?
The solution to 5log_{10}(x)+3log_{10}(y) is log_{10}(x^5y^3)