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

The solution to 2log_{10}(x)-5log_{10}(y) is log_{10}((x^2)/(y^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} (\frac{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} (\frac{a}{b})

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

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

lo g_{3} (x) - lo g_{9} (4 x)

4 ln (2 x^{3 y})

ln (\frac{4 x}{3 + x})

ln (\frac{45 - 1}{1})

ln (10 e^{4})

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