What is ln(x)+ln(x-4)-2ln(x+1) ?

The solution to ln(x)+ln(x-4)-2ln(x+1) is ln((x(x-4))/((x+1)^2))

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simplify ln(x)+ln(x-4)-2ln(x+1)

simplify

ln (x) + ln (x - 4) - 2 ln (x + 1)

ln (\frac{x ( x - 4 )}{( x + 1 ) ^{2}})

Solution steps

ln (x) + ln (x - 4) - 2 ln (x + 1)

Apply log rule:

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

ln (x) + ln (x - 4) = ln (x (x - 4))

= ln (x (x - 4)) - 2 ln (x + 1)

Apply log rule:

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

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

= ln (x (x - 4)) - ln ((x + 1)^{2})

Apply log rule:

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

ln (x (x - 4)) - ln ((x + 1)^{2}) = ln (\frac{x ( x - 4 )}{( x + 1 ) ^{2}})

= ln (\frac{x ( x - 4 )}{( x + 1 ) ^{2}})

\frac{1}{2} (lo g_{10} (b) - lo g_{10} (c))

lo g_{10} (5 bm)

6 ln (x + 7) - ln (x)

lo g_{10} (\frac{x y ^{8}}{z ^{5}})

2 lo g_{10} (2) - lo g_{10} (3)

What is ln(x)+ln(x-4)-2ln(x+1) ?
The solution to ln(x)+ln(x-4)-2ln(x+1) is ln((x(x-4))/((x+1)^2))