What is 7log_{a}(z)-1/5 log_{a}(y)+5log_{a}(x) ?

The solution to 7log_{a}(z)-1/5 log_{a}(y)+5log_{a}(x) is log_{a}((z^7x^5y^{4/5})/y)

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simplify 7log_{a}(z)-1/5 log_{a}(y)+5log_{a}(x)

simplify

7 lo g_{a} (z) - \frac{1}{5} lo g_{a} (y) + 5 lo g_{a} (x)

lo g_{a} (\frac{z ^{7} x ^{5} y ^{\frac{4}{5}}}{y})

Solution steps

7 lo g_{a} (z) - \frac{1}{5} lo g_{a} (y) + 5 lo g_{a} (x)

Apply log rule:

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

7 lo g_{a} (z) = lo g_{a} (z^{7})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{z ^{7}}{y ^{\frac{1}{5}}} : \frac{z ^{7} y ^{\frac{4}{5}}}{y}

= lo g_{a} (\frac{z ^{7} y ^{\frac{4}{5}}}{y}) + 5 lo g_{a} (x)

Apply log rule:

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

5 lo g_{a} (x) = lo g_{a} (x^{5})

= lo g_{a} (\frac{z ^{7} y ^{\frac{4}{5}}}{y}) + lo g_{a} (x^{5})

Apply log rule:

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

lo g_{a} (\frac{z ^{7} y ^{\frac{4}{5}}}{y}) + lo g_{a} (x^{5}) = lo g_{a} (\frac{z ^{7} y ^{\frac{4}{5}}}{y} x^{5})

= lo g_{a} (\frac{z ^{7} y ^{\frac{4}{5}}}{y} x^{5})

Simplify

\frac{z ^{7} y ^{\frac{4}{5}}}{y} x^{5} : \frac{z ^{7} x ^{5} y ^{\frac{4}{5}}}{y}

= lo g_{a} (\frac{z ^{7} x ^{5} y ^{\frac{4}{5}}}{y})

ln (2 π \frac{L}{g})

ln (e^{- n x} x^{a} b)

\frac{1}{4} (ln (\frac{1}{2}) - ln (\frac{1}{4}))

ln (\frac{1024 + 220000 + ( 24 )}{15000})

lo g_{10} (y z^{4})

What is 7log_{a}(z)-1/5 log_{a}(y)+5log_{a}(x) ?
The solution to 7log_{a}(z)-1/5 log_{a}(y)+5log_{a}(x) is log_{a}((z^7x^5y^{4/5})/y)