What is 2ln(x+2)-ln(x+2)-ln(2)-3 ?

The solution to 2ln(x+2)-ln(x+2)-ln(2)-3 is ln((x+2)/2)-3

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simplify 2ln(x+2)-ln(x+2)-ln(2)-3

simplify

2 ln (x + 2) - ln (x + 2) - ln (2) - 3

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

Solution steps

2 ln (x + 2) - ln (x + 2) - ln (2) - 3

Rewrite

- ln (x + 2) - ln (2)

- (ln (x + 2) + ln (2))

= 2 ln (x + 2) - (ln (x + 2) + ln (2)) - 3

Apply log rule:

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

ln (x + 2) + ln (2) = ln (2 (x + 2))

= 2 ln (x + 2) - ln ((x + 2) \cdot 2) - 3

Apply log rule:

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

2 ln (x + 2) = ln ((x + 2)^{2})

= ln ((x + 2)^{2}) - ln (2 (x + 2)) - 3

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

Cancel the common factor:

x + 2

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

ln (\frac{x ^{p} e ^{- y}}{z})

ln (x^{5} y^{3})

lo g_{10} (5 + x) - 2 lo g_{10} (x + 4)

lo g_{10} (x) - lo g_{10} (y)

lo g_{4} (x^{2} - 1) - 5 lo g_{4} (x + 1)

What is 2ln(x+2)-ln(x+2)-ln(2)-3 ?
The solution to 2ln(x+2)-ln(x+2)-ln(2)-3 is ln((x+2)/2)-3