What is 1/2 ln(x+3)+1/2 ln(x+2) ?

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

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simplify 1/2 ln(x+3)+1/2 ln(x+2)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

\frac{1}{2} ln (x + 2) = ln ((x + 2)^{\frac{1}{2}})

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

Apply log rule:

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

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

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

lo g_{2} (\frac{1}{x}) - lo g_{2} (\frac{1}{x ^{2}})

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

\frac{4}{5} ln (x) - 2 ln (y^{4}) + 5 ln (w) - 7 ln (z)

lo g_{2} (5) + lo g_{2} (3)

lo g_{b} (\frac{x ^{3} y}{z ^{4}})

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