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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{f} (\frac{s t ^{8}}{r ^{5}})

lo g_{5} ((x + 10) (x - 10))

2 [lo g_{3} (20) - lo g_{3} (4)] + \frac{1}{2} lo g_{3} (4)

2 ln (x) + 3 ln (y) - 6 ln (z)

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