What is 3log_{c}(y)-15/4 log_{c}(x) ?

The solution to 3log_{c}(y)-15/4 log_{c}(x) is log_{c}((y^3)/(x^{15/4)})

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simplify 3log_{c}(y)-15/4 log_{c}(x)

simplify

3 lo g_{c} (y) - \frac{15}{4} lo g_{c} (x)

lo g_{c} (\frac{y ^{3}}{x ^{\frac{15}{4}}})

Solution steps

3 lo g_{c} (y) - \frac{15}{4} lo g_{c} (x)

Apply log rule:

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

3 lo g_{c} (y) = lo g_{c} (y^{3})

= lo g_{c} (y^{3}) - \frac{15}{4} lo g_{c} (x)

Apply log rule:

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

\frac{15}{4} lo g_{c} (x) = lo g_{c} (x^{\frac{15}{4}})

= lo g_{c} (y^{3}) - lo g_{c} (x^{\frac{15}{4}})

Apply log rule:

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

lo g_{c} (y^{3}) - lo g_{c} (x^{\frac{15}{4}}) = lo g_{c} (\frac{y ^{3}}{x ^{\frac{15}{4}}})

= lo g_{c} (\frac{y ^{3}}{x ^{\frac{15}{4}}})

\frac{1}{3} (6 ln (x + 5) + ln (x) - ln (x^{2} - 6))

1.464 - lo g_{10} (\frac{1}{1 0 ^{0.3}})

\frac{( ln ( 2 ) \cdot 45 )}{ln ( 10 ) - ln ( 2 )}

- 20 lo g_{10} (0.2 1 - 0.01)

lo g_{10} (\frac{4 p ^{3}}{5 q ^{4}})

What is 3log_{c}(y)-15/4 log_{c}(x) ?
The solution to 3log_{c}(y)-15/4 log_{c}(x) is log_{c}((y^3)/(x^{15/4)})