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

The solution to 4ln(2)+2ln(x)-1/2 ln(x+2) is ln((16x^2sqrt(x+2))/(x+2))

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

simplify

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

ln (\frac{16 x ^{2} x + 2}{x + 2})

Solution steps

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

Apply log rule:

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

4 ln (2) = ln (2^{4})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2^{4} = 16

= ln (16 x^{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 (16 x^{2}) - ln ((x + 2)^{\frac{1}{2}})

Apply log rule:

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

ln (16 x^{2}) - ln ((x + 2)^{\frac{1}{2}}) = ln (\frac{16 x ^{2}}{( x + 2 ) ^{\frac{1}{2}}})

= ln (\frac{16 x ^{2}}{( x + 2 ) ^{\frac{1}{2}}})

Simplify

\frac{16 x ^{2}}{( x + 2 ) ^{\frac{1}{2}}} : \frac{16 x ^{2} x + 2}{x + 2}

= ln (\frac{16 x ^{2} x + 2}{x + 2})

(\frac{20.5 \cdot 33.2}{12.8}) ln (12.8 \cdot 1 0^{- 3})

ln (\frac{3000}{ln ( 3 )})

- lo g_{10} (1.26 x 1 0^{- 3})

lo g_{6} (m) + \frac{2}{3} lo g_{6} (n)

ln (x) + 5 \cdot ln (y) - 6 \cdot ln (z)

What is 4ln(2)+2ln(x)-1/2 ln(x+2) ?
The solution to 4ln(2)+2ln(x)-1/2 ln(x+2) is ln((16x^2sqrt(x+2))/(x+2))