What is ln(((sqrt(16+x^2)+x))/4) ?

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

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simplify ln(((sqrt(16+x^2)+x))/4)

simplify

ln (\frac{( 16 + x ^{2} + x )}{4})

ln (16 + x^{2} + x) - 2 ln (2)

Solution steps

ln (\frac{( 16 + x ^{2} + x )}{4})

Apply log rule:

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

ln (\frac{( 16 + x ^{2} + x )}{4}) = ln ((16 + x^{2} + x)) - ln (4)

= ln (x + x^{2} + 16) - ln (4)

ln (4) = 2 ln (2)

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

\frac{ln ( 1155.685 ) - ln ( 1094.66 )}{2}

2000 ln (\frac{3}{2})

\frac{5 ln ( 5 )}{4 ln ( 3 ) - 2 ln ( 5 )}

- 0.287 \cdot ln (\frac{100}{1000})

ln (x^{6} y)

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