What is 0.5ln(400+x)+0.5ln(-400+x) ?

The solution to 0.5ln(400+x)+0.5ln(-400+x) is ln((400+x)^{0.5}(-400+x)^{0.5})

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simplify 0.5ln(400+x)+0.5ln(-400+x)

simplify

0.5 ln (400 + x) + 0.5 ln (- 400 + x)

ln ((400 + x)^{0.5} (- 400 + x)^{0.5})

Solution steps

0.5 ln (400 + x) + 0.5 ln (- 400 + x)

Apply log rule:

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

0.5 ln (x + 400) = ln ((x + 400)^{0.5})

= ln ((x + 400)^{0.5}) + 0.5 ln (x - 400)

Apply log rule:

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

0.5 ln (x - 400) = ln ((x - 400)^{0.5})

= ln ((x + 400)^{0.5}) + ln ((x - 400)^{0.5})

Apply log rule:

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

ln ((400 + x)^{0.5}) + ln ((- 400 + x)^{0.5}) = ln ((x + 400)^{0.5} (x - 400)^{0.5})

= ln ((400 + x)^{0.5} (- 400 + x)^{0.5})

lo g_{e} (362)

ln (\frac{31}{53})

ln (x) + ln (99)

- lo g_{10} (1.4 \cdot 1 0^{- 2})

ln (\frac{106}{14})

What is 0.5ln(400+x)+0.5ln(-400+x) ?
The solution to 0.5ln(400+x)+0.5ln(-400+x) is ln((400+x)^{0.5}(-400+x)^{0.5})