What is 2log_{b}(w)+4(log_{b}(x)-5log_{b}(z)) ?

The solution to 2log_{b}(w)+4(log_{b}(x)-5log_{b}(z)) is log_{b}((w^2x^4)/(z^{20)})

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simplify 2log_{b}(w)+4(log_{b}(x)-5log_{b}(z))

simplify

2 lo g_{b} (w) + 4 (lo g_{b} (x) - 5 lo g_{b} (z))

lo g_{b} (\frac{w ^{2} x ^{4}}{z ^{20}})

Solution steps

2 lo g_{b} (w) + 4 (lo g_{b} (x) - 5 lo g_{b} (z))

Apply log rule:

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

5 lo g_{b} (z) = lo g_{b} (z^{5})

= 2 lo g_{b} (w) + 4 (lo g_{b} (x) - lo g_{b} (z^{5}))

Apply log rule:

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

lo g_{b} (x) - lo g_{b} (z^{5}) = lo g_{b} (\frac{x}{z ^{5}})

= 2 lo g_{b} (w) + 4 lo g_{b} (\frac{x}{z ^{5}})

Apply log rule:

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

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

= lo g_{b} (w^{2}) + 4 lo g_{b} (\frac{x}{z ^{5}})

Apply log rule:

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

4 lo g_{b} (\frac{x}{z ^{5}}) = lo g_{b} ((\frac{x}{z ^{5}})^{4})

= lo g_{b} (w^{2}) + lo g_{b} ((\frac{x}{z ^{5}})^{4})

Apply log rule:

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

lo g_{b} (w^{2}) + lo g_{b} ((\frac{x}{z ^{5}})^{4}) = lo g_{b} ((\frac{x}{z ^{5}})^{4} w^{2})

= lo g_{b} ((\frac{x}{z ^{5}})^{4} w^{2})

Simplify

w^{2} (\frac{x}{z ^{5}})^{4} : \frac{w ^{2} x ^{4}}{z ^{20}}

= lo g_{b} (\frac{w ^{2} x ^{4}}{z ^{20}})

lo g_{6} (\frac{x ^{3}}{y ^{6}})

lo g_{2} (\frac{15}{y})

lo g_{2} (x) + lo g_{2} (x + 15) + lo g_{2} (16)

2 lo g_{3} (6) - lo g_{3} (8)

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

What is 2log_{b}(w)+4(log_{b}(x)-5log_{b}(z)) ?
The solution to 2log_{b}(w)+4(log_{b}(x)-5log_{b}(z)) is log_{b}((w^2x^4)/(z^{20)})