What is 3ln(2)+2ln(x)-12ln(x+4) ?

The solution to 3ln(2)+2ln(x)-12ln(x+4) is ln((8x^2)/((x+4)^{12)})

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simplify 3ln(2)+2ln(x)-12ln(x+4)

simplify

3 ln (2) + 2 ln (x) - 12 ln (x + 4)

ln (\frac{8 x ^{2}}{( x + 4 ) ^{12}})

Solution steps

3 ln (2) + 2 ln (x) - 12 ln (x + 4)

Apply log rule:

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

3 ln (2) = ln (2^{3})

= ln (2^{3}) + 2 ln (x) - 12 ln (x + 4)

Apply log rule:

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

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

= ln (2^{3}) + ln (x^{2}) - 12 ln (x + 4)

Apply log rule:

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

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

= ln (2^{3} x^{2}) - 12 ln (x + 4)

2^{3} = 8

= ln (8 x^{2}) - 12 ln (x + 4)

Apply log rule:

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

12 ln (x + 4) = ln ((x + 4)^{12})

= ln (8 x^{2}) - ln ((x + 4)^{12})

Apply log rule:

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

ln (8 x^{2}) - ln ((x + 4)^{12}) = ln (\frac{8 x ^{2}}{( x + 4 ) ^{12}})

= ln (\frac{8 x ^{2}}{( x + 4 ) ^{12}})

3 lo g_{2} (x) + lo g_{2} (y) - 5 lo g_{2} (z)

lo g_{5} (1000) + lo g_{4 a} (64 a^{3})

lo g_{3^{x}} (+ 2 lo g_{3^{y} - l o g_{3^{z}} (x)} (x))

ln (\frac{e ^{- x} - e ^{x}}{e ^{x} + e ^{- x}})

\frac{1}{10} ln (\frac{5665.74}{5000})

What is 3ln(2)+2ln(x)-12ln(x+4) ?
The solution to 3ln(2)+2ln(x)-12ln(x+4) is ln((8x^2)/((x+4)^{12)})