What is 7log_{10}(x)-12log_{10}(y) ?

The solution to 7log_{10}(x)-12log_{10}(y) is log_{10}((x^7)/(y^{12)})

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simplify 7log_{10}(x)-12log_{10}(y)

simplify

7 lo g_{10} (x) - 12 lo g_{10} (y)

lo g_{10} (\frac{x ^{7}}{y ^{12}})

Solution steps

7 lo g_{10} (x) - 12 lo g_{10} (y)

Apply log rule:

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

7 lo g_{10} (x) = lo g_{10} (x^{7})

= lo g_{10} (x^{7}) - 12 lo g_{10} (y)

Apply log rule:

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

12 lo g_{10} (y) = lo g_{10} (y^{12})

= lo g_{10} (x^{7}) - lo g_{10} (y^{12})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (x^{7}) - lo g_{10} (y^{12}) = lo g_{10} (\frac{x ^{7}}{y ^{12}})

= lo g_{10} (\frac{x ^{7}}{y ^{12}})

ln (\frac{\frac{1}{0.10225}}{35})

ln (\frac{x y ^{4}}{z ^{3}})

ln (y) - \frac{1}{2} (ln (1 + y) - ln (1 - y))

ln (\frac{sin ( 6 x )}{cos ( 15 x )})

ln (\frac{2 - ( 1 )}{1 + 2})

What is 7log_{10}(x)-12log_{10}(y) ?
The solution to 7log_{10}(x)-12log_{10}(y) is log_{10}((x^7)/(y^{12)})