What is 4log_{c}(y)-14/3 log_{c}(x) ?

The solution to 4log_{c}(y)-14/3 log_{c}(x) is log_{c}((y^4)/(x^{14/3)})

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simplify 4log_{c}(y)-14/3 log_{c}(x)

simplify

4 lo g_{c} (y) - \frac{14}{3} lo g_{c} (x)

lo g_{c} (\frac{y ^{4}}{x ^{\frac{14}{3}}})

Solution steps

4 lo g_{c} (y) - \frac{14}{3} lo g_{c} (x)

Apply log rule:

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

4 lo g_{c} (y) = lo g_{c} (y^{4})

= lo g_{c} (y^{4}) - \frac{14}{3} lo g_{c} (x)

Apply log rule:

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

\frac{14}{3} lo g_{c} (x) = lo g_{c} (x^{\frac{14}{3}})

= lo g_{c} (y^{4}) - lo g_{c} (x^{\frac{14}{3}})

Apply log rule:

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

lo g_{c} (y^{4}) - lo g_{c} (x^{\frac{14}{3}}) = lo g_{c} (\frac{y ^{4}}{x ^{\frac{14}{3}}})

= lo g_{c} (\frac{y ^{4}}{x ^{\frac{14}{3}}})

ln (130) - ln (5)

\frac{1}{3} lo g_{8} (7)

ln (7) - (\frac{2}{3}) \cdot ln (2) + ln (3)

ln (4 e^{i})

ln (\frac{10000}{1000000})

What is 4log_{c}(y)-14/3 log_{c}(x) ?
The solution to 4log_{c}(y)-14/3 log_{c}(x) is log_{c}((y^4)/(x^{14/3)})