What is 6log_{10}(x)+2log_{10}(y) ?

The solution to 6log_{10}(x)+2log_{10}(y) is log_{10}(x^6y^2)

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simplify 6log_{10}(x)+2log_{10}(y)

simplify

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

lo g_{10} (x^{6} y^{2})

Solution steps

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

Apply log rule:

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

6 lo g_{10} (x) = lo g_{10} (x^{6})

= lo g_{10} (x^{6}) + 2 lo g_{10} (y)

Apply log rule:

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

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

= lo g_{10} (x^{6}) + lo g_{10} (y^{2})

Apply log rule:

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

lo g_{10} (x^{6}) + lo g_{10} (y^{2}) = lo g_{10} (x^{6} y^{2})

= lo g_{10} (x^{6} y^{2})

lo g_{2} (x) - lo g_{2} (y) - 3 lo g_{2} (z)

lo g_{10} (y) + 6 lo g_{10} (z)

lo g_{4} (\frac{y}{x})

lo g_{5} (7 x)

What is 6log_{10}(x)+2log_{10}(y) ?
The solution to 6log_{10}(x)+2log_{10}(y) is log_{10}(x^6y^2)