What is 4log_{b}(x+3)-2log_{b}(x+2)+log_{b}(x) ?

The solution to 4log_{b}(x+3)-2log_{b}(x+2)+log_{b}(x) is log_{b}((x(x+3)^4)/((x+2)^2))

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simplify 4log_{b}(x+3)-2log_{b}(x+2)+log_{b}(x)

simplify

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

lo g_{b} (\frac{x ( x + 3 ) ^{4}}{( x + 2 ) ^{2}})

Solution steps

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

Apply log rule:

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

4 lo g_{b} (x + 3) = lo g_{b} ((x + 3)^{4})

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{b} ((x + 3)^{4}) - lo g_{b} ((x + 2)^{2}) = lo g_{b} (\frac{( x + 3 ) ^{4}}{( x + 2 ) ^{2}})

= lo g_{b} (\frac{( x + 3 ) ^{4}}{( x + 2 ) ^{2}}) + lo g_{b} (x)

Apply log rule:

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

lo g_{b} (\frac{( x + 3 ) ^{4}}{( x + 2 ) ^{2}}) + lo g_{b} (x) = lo g_{b} (\frac{( x + 3 ) ^{4}}{( x + 2 ) ^{2}} x)

= lo g_{b} (\frac{( x + 3 ) ^{4}}{( x + 2 ) ^{2}} x)

Multiply fractions:

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

= lo g_{b} (\frac{x ( x + 3 ) ^{4}}{( x + 2 ) ^{2}})

\frac{1}{3} [2 ln (x + 3) + ln (x) + ln (x^{2} - 1)]

3.8 + lo g_{10} (\frac{0.19}{0.41})

lo g_{10} (\frac{y}{100})

ln (\frac{1}{2 x ^{3}})

lo g_{8} (64 x) + lo g_{8} (x)

What is 4log_{b}(x+3)-2log_{b}(x+2)+log_{b}(x) ?
The solution to 4log_{b}(x+3)-2log_{b}(x+2)+log_{b}(x) is log_{b}((x(x+3)^4)/((x+2)^2))