What is 1/9 (7log_{c}(x)-log_{c}(y^9z^5)) ?

The solution to 1/9 (7log_{c}(x)-log_{c}(y^9z^5)) is 1/9 log_{c}((x^7)/(y^9z^5))

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simplify 1/9 (7log_{c}(x)-log_{c}(y^9z^5))

simplify

\frac{1}{9} (7 lo g_{c} (x) - lo g_{c} (y^{9} z^{5}))

\frac{1}{9} lo g_{c} (\frac{x ^{7}}{y ^{9} z ^{5}})

Solution steps

\frac{1}{9} (7 lo g_{c} (x) - lo g_{c} (y^{9} z^{5}))

Apply log rule:

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

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

= \frac{1}{9} (lo g_{c} (x^{7}) - lo g_{c} (y^{9} z^{5}))

Apply log rule:

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

lo g_{c} (x^{7}) - lo g_{c} (y^{9} z^{5}) = lo g_{c} (\frac{x ^{7}}{y ^{9} z ^{5}})

= \frac{1}{9} lo g_{c} (\frac{x ^{7}}{y ^{9} z ^{5}})

3 ln (x + 4) - ln (x)

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

lo g_{10} (\frac{x ^{15} y ^{13}}{z ^{19}})

lo g_{3} (y) - lo g_{3} (4)

lo g_{b} (\frac{x ^{2} y}{z ^{3}})

What is 1/9 (7log_{c}(x)-log_{c}(y^9z^5)) ?
The solution to 1/9 (7log_{c}(x)-log_{c}(y^9z^5)) is 1/9 log_{c}((x^7)/(y^9z^5))