What is expand log_{b}(5)+2log_{b}(2) ?

The solution to expand log_{b}(5)+2log_{b}(2) is log_{b}(20)

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expand log_{b}(5)+2log_{b}(2)

expand

lo g_{b} (5) + 2 lo g_{b} (2)

lo g_{b} (20)

Solution steps

lo g_{b} (5) + 2 lo g_{b} (2)

Apply log rule:

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

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

= lo g_{b} (5) + lo g_{b} (2^{2})

Apply log rule:

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

lo g_{b} (5) + lo g_{b} (2^{2}) = lo g_{b} (2^{2} \cdot 5)

= lo g_{b} (2^{2} \cdot 5)

Expand

5 \cdot 2^{2} : 20

= lo g_{b} (20)

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\frac{1}{2} ln (20) - \frac{1}{2} ln (8)

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What is expand log_{b}(5)+2log_{b}(2) ?
The solution to expand log_{b}(5)+2log_{b}(2) is log_{b}(20)