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

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

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

simplify

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

lo g_{c} (\frac{w ^{2} x ^{7} z}{z})

Solution steps

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

Apply log rule:

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

2 lo g_{c} (w) = lo g_{c} (w^{2})

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

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

Apply log rule:

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

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

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

Simplify

\frac{w ^{2}}{z ^{\frac{1}{2}}} : \frac{w ^{2} z}{z}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{w ^{2} z}{z} x^{7} : \frac{w ^{2} x ^{7} z}{z}

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

ln ((\frac{3 y ^{3} - 3}{x ^{3}})^{- \frac{2}{9}}) - ln (x)

lo g_{10} (\frac{4}{5 x})

3 ln (2) + 2 ln (x) - \frac{1}{2} ln (x - 4)

ln (\frac{p}{( 1 - p )})

2 ln (x) + ln (y) - 4 x - y

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