What is ln((5x)/(sqrt(x^2-4))) ?

The solution to ln((5x)/(sqrt(x^2-4))) is ln(5)+ln(x)-ln(sqrt(x^2-4))

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simplify ln((5x)/(sqrt(x^2-4)))

simplify

ln (\frac{5 x}{x ^{2} - 4})

ln (5) + ln (x) - ln (x^{2} - 4)

Solution steps

ln (\frac{5 x}{x ^{2} - 4})

Apply log rule:

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

ln (\frac{5 x}{x ^{2} - 4}) = ln (5 x) - ln (x^{2} - 4)

= ln (5 x) - ln (x^{2} - 4)

Apply log rule:

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

ln (5 x) = ln (5) + ln (x)

= ln (5) + ln (x) - ln (x^{2} - 4)

4 ln (x + 1) - 3 ln (y)

ln (\frac{x ^{2} - 4 x + 3}{x ^{2} - 5 x + 6})

- \frac{9}{14} \cdot lo g_{2} (\frac{9}{14}) - \frac{5}{14} \cdot lo g_{2} (\frac{5}{14})

What is ln((5x)/(sqrt(x^2-4))) ?
The solution to ln((5x)/(sqrt(x^2-4))) is ln(5)+ln(x)-ln(sqrt(x^2-4))