What is 2log_{c}(z)-1/5 log_{c}(y)+6log_{c}(x) ?

The solution to 2log_{c}(z)-1/5 log_{c}(y)+6log_{c}(x) is log_{c}((z^2x^6y^{4/5})/y)

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simplify 2log_{c}(z)-1/5 log_{c}(y)+6log_{c}(x)

simplify

2 lo g_{c} (z) - \frac{1}{5} lo g_{c} (y) + 6 lo g_{c} (x)

lo g_{c} (\frac{z ^{2} x ^{6} y ^{\frac{4}{5}}}{y})

Solution steps

2 lo g_{c} (z) - \frac{1}{5} lo g_{c} (y) + 6 lo g_{c} (x)

Apply log rule:

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

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

= lo g_{c} (z^{2}) - \frac{1}{5} lo g_{c} (y) + 6 lo g_{c} (x)

Apply log rule:

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

\frac{1}{5} lo g_{c} (y) = lo g_{c} (y^{\frac{1}{5}})

= lo g_{c} (z^{2}) - lo g_{c} (y^{\frac{1}{5}}) + 6 lo g_{c} (x)

Apply log rule:

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

lo g_{c} (z^{2}) - lo g_{c} (y^{\frac{1}{5}}) = lo g_{c} (\frac{z ^{2}}{y ^{\frac{1}{5}}})

= lo g_{c} (\frac{z ^{2}}{y ^{\frac{1}{5}}}) + 6 lo g_{c} (x)

Simplify

\frac{z ^{2}}{y ^{\frac{1}{5}}} : \frac{z ^{2} y ^{\frac{4}{5}}}{y}

= lo g_{c} (\frac{z ^{2} y ^{\frac{4}{5}}}{y}) + 6 lo g_{c} (x)

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} (\frac{z ^{2} y ^{\frac{4}{5}}}{y}) + lo g_{c} (x^{6})

Apply log rule:

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

lo g_{c} (\frac{z ^{2} y ^{\frac{4}{5}}}{y}) + lo g_{c} (x^{6}) = lo g_{c} (\frac{z ^{2} y ^{\frac{4}{5}}}{y} x^{6})

= lo g_{c} (\frac{z ^{2} y ^{\frac{4}{5}}}{y} x^{6})

Simplify

\frac{z ^{2} y ^{\frac{4}{5}}}{y} x^{6} : \frac{z ^{2} x ^{6} y ^{\frac{4}{5}}}{y}

= lo g_{c} (\frac{z ^{2} x ^{6} y ^{\frac{4}{5}}}{y})

- lo g_{10} (4.25 \cdot 1 0^{- 5})

\frac{1}{3} ln (3 r^{2} s)

0.9 ln (3) + 2.4 ln (0.75)

\frac{3}{4} ln ∣ x + 1 ∣ + \frac{1}{2 x + 2} + \frac{1}{4} ln ∣ x - 1 ∣ + C

\frac{ln ( 1.19 ) - ln ( 1.17 )}{2}

What is 2log_{c}(z)-1/5 log_{c}(y)+6log_{c}(x) ?
The solution to 2log_{c}(z)-1/5 log_{c}(y)+6log_{c}(x) is log_{c}((z^2x^6y^{4/5})/y)