What is simplify-1/2 ln(2+x)-1/2 ln(2-x) ?

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

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

simplify

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

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

Solution steps

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

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

Rewrite

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

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

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

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

ln (θ e^{- n (x^{1} + x^{2} + x^{3})})

ln (\frac{225 - 0.9}{( 2.82108 - 0.9 )})

- \frac{1}{3} ln (\frac{5 + 1}{5 - 2})

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

lo g_{0.5} (x^{2})

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