What is 1/2 log_{10}(x+3)+1/2 log_{10}(x+2) ?

The solution to 1/2 log_{10}(x+3)+1/2 log_{10}(x+2) is log_{10}((x+3)^{1/2}(x+2)^{1/2})

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simplify 1/2 log_{10}(x+3)+1/2 log_{10}(x+2)

simplify

\frac{1}{2} lo g_{10} (x + 3) + \frac{1}{2} lo g_{10} (x + 2)

lo g_{10} ((x + 3)^{\frac{1}{2}} (x + 2)^{\frac{1}{2}})

Solution steps

\frac{1}{2} lo g_{10} (x + 3) + \frac{1}{2} lo g_{10} (x + 2)

Apply log rule:

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

\frac{1}{2} lo g_{10} (x + 3) = lo g_{10} ((x + 3)^{\frac{1}{2}})

= lo g_{10} ((x + 3)^{\frac{1}{2}}) + \frac{1}{2} lo g_{10} (x + 2)

Apply log rule:

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

\frac{1}{2} lo g_{10} (x + 2) = lo g_{10} ((x + 2)^{\frac{1}{2}})

= lo g_{10} ((x + 3)^{\frac{1}{2}}) + lo g_{10} ((x + 2)^{\frac{1}{2}})

Apply log rule:

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

lo g_{10} ((x + 3)^{\frac{1}{2}}) + lo g_{10} ((x + 2)^{\frac{1}{2}}) = lo g_{10} ((x + 3)^{\frac{1}{2}} (x + 2)^{\frac{1}{2}})

= lo g_{10} ((x + 3)^{\frac{1}{2}} (x + 2)^{\frac{1}{2}})

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What is 1/2 log_{10}(x+3)+1/2 log_{10}(x+2) ?
The solution to 1/2 log_{10}(x+3)+1/2 log_{10}(x+2) is log_{10}((x+3)^{1/2}(x+2)^{1/2})