What is ln|x^2+sqrt(1+x^4)|-ln|4+sqrt(17)| ?

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simplify ln|x^2+sqrt(1+x^4)|-ln|4+sqrt(17)|

simplify

ln x^{2} + 1 + x^{4} - ln 4 + 17

ln (- (4 - 17) x^{2} + 1 + x^{4})

Solution steps

ln x^{2} + 1 + x^{4} - ln 4 + 17

Apply log rule:

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

ln x^{2} + 1 + x^{4} - ln 4 + 17 = ln (\frac{x ^{2} + x ^{4} + 1}{4 + 17})

= ln (\frac{x ^{2} + 1 + x ^{4}}{4 + 17})

Simplify

\frac{x ^{2} + 1 + x ^{4}}{4 + 17} : - (4 - 17) x^{2} + 1 + x^{4}

= ln (- (4 - 17) x^{2} + 1 + x^{4})

2 ln (4 x)

lo g_{8} (\frac{( ab ) 3}{c ^{5}})

0.385 \cdot ln (\frac{60 + 273}{24 + 273})

0.9 lo g_{10} (1000) + 0.1 lo g_{10} (500)

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

What is ln|x^2+sqrt(1+x^4)|-ln|4+sqrt(17)| ?
The solution to ln|x^2+sqrt(1+x^4)|-ln|4+sqrt(17)| is ln(-(4-sqrt(17))|x^2+sqrt(1+x^4)|)