What is simplify-4log_{b}(d)+log_{b}(e)-2log_{b}(f) ?

The solution to simplify-4log_{b}(d)+log_{b}(e)-2log_{b}(f) is log_{b}(e/(d^4f^2))

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simplify-4log_{b}(d)+log_{b}(e)-2log_{b}(f)

simplify

- 4 lo g_{b} (d) + lo g_{b} (e) - 2 lo g_{b} (f)

lo g_{b} (\frac{e}{d ^{4} f ^{2}})

Solution steps

- 4 lo g_{b} (d) + lo g_{b} (e) - 2 lo g_{b} (f)

Apply log rule:

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

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

= - lo g_{b} (d^{4}) + lo g_{b} (e) - 2 lo g_{b} (f)

Apply log rule:

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

lo g_{b} (e) - lo g_{b} (d^{4}) = lo g_{b} (\frac{e}{d ^{4}})

= lo g_{b} (\frac{e}{d ^{4}}) - 2 lo g_{b} (f)

Apply log rule:

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

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

= lo g_{b} (\frac{e}{d ^{4}}) - lo g_{b} (f^{2})

Apply log rule:

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

lo g_{b} (\frac{e}{d ^{4}}) - lo g_{b} (f^{2}) = lo g_{b} (\frac{\frac{e}{d ^{4}}}{f ^{2}})

= lo g_{b} (\frac{\frac{e}{d ^{4}}}{f ^{2}})

Apply the fraction rule:

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

= lo g_{b} (\frac{e}{d ^{4} f ^{2}})

lo g_{10} (\frac{3 x}{y})

ln ∣ b ∣ - ln ∣ a ∣

lo g_{2} (64 p)

ln (\frac{11}{6})

What is simplify-4log_{b}(d)+log_{b}(e)-2log_{b}(f) ?
The solution to simplify-4log_{b}(d)+log_{b}(e)-2log_{b}(f) is log_{b}(e/(d^4f^2))