What is 4log_{10}(x)+log_{10}(y) ?

The solution to 4log_{10}(x)+log_{10}(y) is log_{10}(x^4y)

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simplify 4log_{10}(x)+log_{10}(y)

simplify

4 lo g_{10} (x) + lo g_{10} (y)

lo g_{10} (x^{4} y)

Solution steps

4 lo g_{10} (x) + lo g_{10} (y)

Apply log rule:

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

4 lo g_{10} (x) = lo g_{10} (x^{4})

= lo g_{10} (x^{4}) + lo g_{10} (y)

Apply log rule:

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

lo g_{10} (x^{4}) + lo g_{10} (y) = lo g_{10} (x^{4} y)

= lo g_{10} (x^{4} y)

ln (4 x^{2} - 3) - ln (x^{2})

12 + 4 ln (\frac{9}{5})

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

ln (5) + ln (5^{2}) + ln (5^{3})

ln (x^{2} y^{\frac{1}{3}})

What is 4log_{10}(x)+log_{10}(y) ?
The solution to 4log_{10}(x)+log_{10}(y) is log_{10}(x^4y)