What is 3log_{10}(7x)-4log_{10}(7y) ?

The solution to 3log_{10}(7x)-4log_{10}(7y) is log_{10}((x^3)/(7y^4))

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simplify 3log_{10}(7x)-4log_{10}(7y)

simplify

3 lo g_{10} (7 x) - 4 lo g_{10} (7 y)

lo g_{10} (\frac{x ^{3}}{7 y ^{4}})

Solution steps

3 lo g_{10} (7 x) - 4 lo g_{10} (7 y)

3 lo g_{10} (7 x) = lo g_{10} ((7 x)^{3})

- 4 lo g_{10} (7 y) = - lo g_{10} ((7 y)^{4})

= lo g_{10} ((7 x)^{3}) - lo g_{10} ((7 y)^{4})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} ((7 x)^{3}) - lo g_{10} ((7 y)^{4}) = lo g_{10} (\frac{( 7 x ) ^{3}}{( 7 y ) ^{4}})

= lo g_{10} (\frac{( 7 x ) ^{3}}{( 7 y ) ^{4}})

Cancel

\frac{( 7 x ) ^{3}}{( 7 y ) ^{4}} : \frac{x ^{3}}{7 y ^{4}}

= lo g_{10} (\frac{x ^{3}}{7 y ^{4}})

lo g_{2} (\frac{1}{m})

ln (\frac{2}{11})

ln (\frac{2 x ^{3} + 6}{3 x + 4})

ln (- \frac{1}{2} e^{- 2 y})

lo g_{b} (6) + lo g_{b} (10)

What is 3log_{10}(7x)-4log_{10}(7y) ?
The solution to 3log_{10}(7x)-4log_{10}(7y) is log_{10}((x^3)/(7y^4))