What is ln((x+11)/(sqrt(x^3-4))) ?

The solution to ln((x+11)/(sqrt(x^3-4))) is ln(x+11)-ln(sqrt(x^3-4))

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simplify ln((x+11)/(sqrt(x^3-4)))

simplify

ln (\frac{x + 11}{x ^{3} - 4})

ln (x + 11) - ln (x^{3} - 4)

Solution steps

ln (\frac{x + 11}{x ^{3} - 4})

Apply log rule:

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

ln (\frac{x + 11}{x ^{3} - 4}) = ln (x + 11) - ln (x^{3} - 4)

= ln (x + 11) - ln (x^{3} - 4)

2 ln (\frac{5}{3}) - \frac{14}{15}

3 lo g_{b} (x) + 6 lo g_{b} (z)

- lo g_{10} (4.5 \cdot 1 0^{- 5})

ln (125) - 2 ln (5)

- lo g_{10} (5 \cdot 1 0^{- 11})

What is ln((x+11)/(sqrt(x^3-4))) ?
The solution to ln((x+11)/(sqrt(x^3-4))) is ln(x+11)-ln(sqrt(x^3-4))