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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{10} (x) + lo g_{10} (x - 3)

2 ln (2) - ln (3)

2 + \frac{1}{2} lo g_{2} (49) - lo g_{2} (21)

ln (7) + ln (x) + ln (y)

lo g_{2} (\frac{3 x ^{2}}{( x - 1 ) ^{2}})

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