What is 6log_{c}(x)-1/2 log_{c}(z)+7log_{c}(w) ?

The solution to 6log_{c}(x)-1/2 log_{c}(z)+7log_{c}(w) is log_{c}((x^6w^7sqrt(z))/z)

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simplify 6log_{c}(x)-1/2 log_{c}(z)+7log_{c}(w)

simplify

6 lo g_{c} (x) - \frac{1}{2} lo g_{c} (z) + 7 lo g_{c} (w)

lo g_{c} (\frac{x ^{6} w ^{7} z}{z})

Solution steps

6 lo g_{c} (x) - \frac{1}{2} lo g_{c} (z) + 7 lo g_{c} (w)

Apply log rule:

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

6 lo g_{c} (x) = lo g_{c} (x^{6})

= lo g_{c} (x^{6}) - \frac{1}{2} lo g_{c} (z) + 7 lo g_{c} (w)

Apply log rule:

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

\frac{1}{2} lo g_{c} (z) = lo g_{c} (z^{\frac{1}{2}})

= lo g_{c} (x^{6}) - lo g_{c} (z^{\frac{1}{2}}) + 7 lo g_{c} (w)

Apply log rule:

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

lo g_{c} (x^{6}) - lo g_{c} (z^{\frac{1}{2}}) = lo g_{c} (\frac{x ^{6}}{z ^{\frac{1}{2}}})

= lo g_{c} (\frac{x ^{6}}{z ^{\frac{1}{2}}}) + 7 lo g_{c} (w)

Simplify

\frac{x ^{6}}{z ^{\frac{1}{2}}} : \frac{x ^{6} z}{z}

= lo g_{c} (\frac{x ^{6} z}{z}) + 7 lo g_{c} (w)

Apply log rule:

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

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

= lo g_{c} (\frac{x ^{6} z}{z}) + lo g_{c} (w^{7})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{c} (\frac{x ^{6} z}{z}) + lo g_{c} (w^{7}) = lo g_{c} (\frac{x ^{6} z}{z} w^{7})

= lo g_{c} (\frac{x ^{6} z}{z} w^{7})

Simplify

\frac{x ^{6} z}{z} w^{7} : \frac{x ^{6} w ^{7} z}{z}

= lo g_{c} (\frac{x ^{6} w ^{7} z}{z})

ln (\frac{1}{29})

ln (\frac{25}{22.5})

9 x + 3 ln (x - 1) - 3 ln (2) + 4 ln (x)

- 3 ln ∣ x + 3 ∣ + 3 ln ∣ x + 1 ∣

\frac{1}{2} \cdot ln (\frac{0.697}{0.1828})

What is 6log_{c}(x)-1/2 log_{c}(z)+7log_{c}(w) ?
The solution to 6log_{c}(x)-1/2 log_{c}(z)+7log_{c}(w) is log_{c}((x^6w^7sqrt(z))/z)