What is 2log_{b}(x)+1/2 log_{b}(x+4) ?

The solution to 2log_{b}(x)+1/2 log_{b}(x+4) is log_{b}(x^2(x+4)^{1/2})

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simplify 2log_{b}(x)+1/2 log_{b}(x+4)

simplify

2 lo g_{b} (x) + \frac{1}{2} lo g_{b} (x + 4)

lo g_{b} (x^{2} (x + 4)^{\frac{1}{2}})

Solution steps

2 lo g_{b} (x) + \frac{1}{2} lo g_{b} (x + 4)

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}) + \frac{1}{2} lo g_{b} (x + 4)

Apply log rule:

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

\frac{1}{2} lo g_{b} (x + 4) = lo g_{b} ((x + 4)^{\frac{1}{2}})

= lo g_{b} (x^{2}) + lo g_{b} ((x + 4)^{\frac{1}{2}})

Apply log rule:

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

lo g_{b} (x^{2}) + lo g_{b} ((x + 4)^{\frac{1}{2}}) = lo g_{b} (x^{2} (x + 4)^{\frac{1}{2}})

= lo g_{b} (x^{2} (x + 4)^{\frac{1}{2}})

lo g_{10} (20) - lo g_{10} (5)

lo g_{10} (10000 y)

lo g_{10} (x^{2}) - lo g_{10} (y) - lo g_{10} (x)

lo g_{10} (\frac{2}{ab})

lo g_{10} (\frac{z ^{5}}{y x ^{3}})

What is 2log_{b}(x)+1/2 log_{b}(x+4) ?
The solution to 2log_{b}(x)+1/2 log_{b}(x+4) is log_{b}(x^2(x+4)^{1/2})