What is 8ln|sqrt(2+4)-4|+2ln|sqrt(2+4)+1| ?

The solution to 8ln|sqrt(2+4)-4|+2ln|sqrt(2+4)+1| is ln(3145072-1283808sqrt(6))

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simplify 8ln|sqrt(2+4)-4|+2ln|sqrt(2+4)+1|

simplify

8 ln 2 + 4 - 4 + 2 ln 2 + 4 + 1

ln (3145072 - 12838086)

Decimal Notation

5.98512 \dots

Solution steps

8 ln 2 + 4 - 4 + 2 ln 2 + 4 + 1

Apply log rule:

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

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

= ln (2 + 4 - 4^{8}) + 2 ln 2 + 4 + 1

Apply log rule:

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

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

= ln (2 + 4 - 4^{8}) + ln (2 + 4 + 1^{2})

Apply log rule:

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

ln (2 + 4 - 4^{8}) + ln (2 + 4 + 1^{2}) = ln (2 + 4 - 4^{8} 2 + 4 + 1^{2})

= ln (2 + 4 - 4^{8} 2 + 4 + 1^{2})

2 + 4 - 4^{8} 2 + 4 + 1^{2} = 3145072 - 12838086

= ln (3145072 - 12838086)

lo g_{10} (4 5^{\circ} 1 2^{\circ} 9^{\circ})

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ln (\frac{x y ^{4}}{z ^{3}})

ln (\frac{2}{2 \cdot ( 1.42 \cdot 1 0 ^{(- 3)} )})

ln (\frac{1}{m} e^{\frac{- ( x - 2 )}{m}})

What is 8ln|sqrt(2+4)-4|+2ln|sqrt(2+4)+1| ?
The solution to 8ln|sqrt(2+4)-4|+2ln|sqrt(2+4)+1| is ln(3145072-1283808sqrt(6))