What is 12log_{10}(5x)-6log_{10}(5y) ?

The solution to 12log_{10}(5x)-6log_{10}(5y) is log_{10}((15625x^{12})/(y^6))

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simplify 12log_{10}(5x)-6log_{10}(5y)

simplify

12 lo g_{10} (5 x) - 6 lo g_{10} (5 y)

lo g_{10} (\frac{15625 x ^{12}}{y ^{6}})

Solution steps

12 lo g_{10} (5 x) - 6 lo g_{10} (5 y)

12 lo g_{10} (5 x) = lo g_{10} ((5 x)^{12})

- 6 lo g_{10} (5 y) = - lo g_{10} ((5 y)^{6})

= lo g_{10} ((5 x)^{12}) - lo g_{10} ((5 y)^{6})

Apply log rule:

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

lo g_{10} ((5 x)^{12}) - lo g_{10} ((5 y)^{6}) = lo g_{10} (\frac{( 5 x ) ^{12}}{( 5 y ) ^{6}})

= lo g_{10} (\frac{( 5 x ) ^{12}}{( 5 y ) ^{6}})

Cancel

\frac{( 5 x ) ^{12}}{( 5 y ) ^{6}} : \frac{15625 x ^{12}}{y ^{6}}

= lo g_{10} (\frac{15625 x ^{12}}{y ^{6}})

- 5 ln (x) - 5 ln (y)

1 - ln (6) + ln (3)

ln (\frac{15}{10})

ln (\frac{1}{0.14})

ln (c x^{6})

What is 12log_{10}(5x)-6log_{10}(5y) ?
The solution to 12log_{10}(5x)-6log_{10}(5y) is log_{10}((15625x^{12})/(y^6))