What is 2log_{10}(x)-7log_{10}(y) ?

The solution to 2log_{10}(x)-7log_{10}(y) is log_{10}((x^2)/(y^7))

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simplify 2log_{10}(x)-7log_{10}(y)

simplify

2 lo g_{10} (x) - 7 lo g_{10} (y)

lo g_{10} (\frac{x ^{2}}{y ^{7}})

Solution steps

2 lo g_{10} (x) - 7 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}) - 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^{2}) - lo g_{10} (y^{7})

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^{7}) = lo g_{10} (\frac{x ^{2}}{y ^{7}})

= lo g_{10} (\frac{x ^{2}}{y ^{7}})

ln (x^{5}) - ln (x)

\frac{1}{2} lo g_{b} (57) + \frac{1}{2} lo g_{b} (74)

ln (2 e^{2 x})

lo g_{10} ((u v^{6})^{4})

ln (\frac{197}{760})

What is 2log_{10}(x)-7log_{10}(y) ?
The solution to 2log_{10}(x)-7log_{10}(y) is log_{10}((x^2)/(y^7))