What is 4log_{10}(x)+7log_{10}(y) ?

The solution to 4log_{10}(x)+7log_{10}(y) is log_{10}(x^4y^7)

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simplify 4log_{10}(x)+7log_{10}(y)

simplify

4 lo g_{10} (x) + 7 lo g_{10} (y)

lo g_{10} (x^{4} y^{7})

Solution steps

4 lo g_{10} (x) + 7 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}) + 7 lo g_{10} (y)

Apply log rule:

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

7 lo g_{10} (y) = lo g_{10} (y^{7})

= lo g_{10} (x^{4}) + lo g_{10} (y^{7})

Apply log rule:

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

lo g_{10} (x^{4}) + lo g_{10} (y^{7}) = lo g_{10} (x^{4} y^{7})

= lo g_{10} (x^{4} y^{7})

lo g_{5} (\frac{25}{x + 3})

2 ln (ln (e^{z}) ln (e^{y})) - ln (x^{2})

lo g_{a} (\frac{2}{5})

4.74 + lo g_{10} (\frac{0.2}{0.3})

lo g_{b} (\frac{x ^{3} y}{z ^{7}})

What is 4log_{10}(x)+7log_{10}(y) ?
The solution to 4log_{10}(x)+7log_{10}(y) is log_{10}(x^4y^7)