What is 3log_{b}(x)-6log_{b}(z)-4log_{b}(w) ?

The solution to 3log_{b}(x)-6log_{b}(z)-4log_{b}(w) is log_{b}((x^3)/(z^6w^4))

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simplify 3log_{b}(x)-6log_{b}(z)-4log_{b}(w)

simplify

3 lo g_{b} (x) - 6 lo g_{b} (z) - 4 lo g_{b} (w)

lo g_{b} (\frac{x ^{3}}{z ^{6} w ^{4}})

Solution steps

3 lo g_{b} (x) - 6 lo g_{b} (z) - 4 lo g_{b} (w)

Apply log rule:

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

3 lo g_{b} (x) = lo g_{b} (x^{3})

= lo g_{b} (x^{3}) - 6 lo g_{b} (z) - 4 lo g_{b} (w)

Apply log rule:

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

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

= lo g_{b} (x^{3}) - lo g_{b} (z^{6}) - 4 lo g_{b} (w)

Apply log rule:

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

lo g_{b} (x^{3}) - lo g_{b} (z^{6}) = lo g_{b} (\frac{x ^{3}}{z ^{6}})

= lo g_{b} (\frac{x ^{3}}{z ^{6}}) - 4 lo g_{b} (w)

Apply log rule:

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

4 lo g_{b} (w) = lo g_{b} (w^{4})

= lo g_{b} (\frac{x ^{3}}{z ^{6}}) - lo g_{b} (w^{4})

Apply log rule:

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

lo g_{b} (\frac{x ^{3}}{z ^{6}}) - lo g_{b} (w^{4}) = lo g_{b} (\frac{\frac{x ^{3}}{z ^{6}}}{w ^{4}})

= lo g_{b} (\frac{\frac{x ^{3}}{z ^{6}}}{w ^{4}})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= lo g_{b} (\frac{x ^{3}}{z ^{6} w ^{4}})

4 + 2 lo g_{5} (x) - \frac{1}{3} lo g_{5} (y)

- ln (\frac{2 l + d}{l}) + ln (\frac{l + d}{l}) + ln (\frac{l + d}{d})

- lo g_{10} (7.93 \cdot 1 0^{- 3})

\frac{2}{7} lo g_{10} (a) - \frac{1}{8} lo g_{10} (b)

ln (ln (y)) + ln (x) + c

What is 3log_{b}(x)-6log_{b}(z)-4log_{b}(w) ?
The solution to 3log_{b}(x)-6log_{b}(z)-4log_{b}(w) is log_{b}((x^3)/(z^6w^4))