What is simplify-2log_{b}(x)-6log_{b}(y)+1/7 log_{b}(z) ?

The solution to simplify-2log_{b}(x)-6log_{b}(y)+1/7 log_{b}(z) is log_{b}((z^{1/7})/(x^2y^6))

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simplify-2log_{b}(x)-6log_{b}(y)+1/7 log_{b}(z)

simplify

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

lo g_{b} (\frac{z ^{\frac{1}{7}}}{x ^{2} y ^{6}})

Solution steps

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

Apply log rule:

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

2 lo g_{b} (x) = lo g_{b} (x^{2})

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

Apply log rule:

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

6 lo g_{b} (y) = lo g_{b} (y^{6})

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

Rewrite

- lo g_{b} (x^{2}) - lo g_{b} (y^{6})

- (lo g_{b} (x^{2}) + lo g_{b} (y^{6}))

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

Apply log rule:

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

lo g_{b} (x^{2}) + lo g_{b} (y^{6}) = lo g_{b} (x^{2} y^{6})

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

Apply log rule:

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

\frac{1}{7} lo g_{b} (z) = lo g_{b} (z^{\frac{1}{7}})

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

Apply log rule:

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

lo g_{b} (z^{\frac{1}{7}}) - lo g_{b} (x^{2} y^{6}) = lo g_{b} (\frac{z ^{\frac{1}{7}}}{x ^{2} y ^{6}})

= lo g_{b} (\frac{z ^{\frac{1}{7}}}{x ^{2} y ^{6}})

ln ((x^{2} + 1) (x - 1))

lo g_{8} (7 x^{4})

lo g_{9} (u^{2})

lo g_{4} (2 x^{2} + x - 21) - lo g_{4} (x - 3)

4 lo g_{a} (y) - \frac{1}{2} lo g_{a} (x) + 3 lo g_{a} (w)

What is simplify-2log_{b}(x)-6log_{b}(y)+1/7 log_{b}(z) ?
The solution to simplify-2log_{b}(x)-6log_{b}(y)+1/7 log_{b}(z) is log_{b}((z^{1/7})/(x^2y^6))