What is 5log_{10}(x)+2log_{10}(y) ?

The solution to 5log_{10}(x)+2log_{10}(y) is log_{10}(x^5y^2)

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simplify 5log_{10}(x)+2log_{10}(y)

simplify

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

lo g_{10} (x^{5} y^{2})

Solution steps

5 lo g_{10} (x) + 2 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}) + 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^{5}) + lo g_{10} (y^{2})

Apply log rule:

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

lo g_{10} (x^{5}) + lo g_{10} (y^{2}) = lo g_{10} (x^{5} y^{2})

= lo g_{10} (x^{5} y^{2})

lo g_{b} (2) + 2 lo g_{b} (5)

ln (e i)

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

lo g_{5} (\frac{y}{25})

2 ln (x) - 3 ln (y) + 4 ln (t)

What is 5log_{10}(x)+2log_{10}(y) ?
The solution to 5log_{10}(x)+2log_{10}(y) is log_{10}(x^5y^2)