What is ln((6x)/(sqrt(x^2-4))) ?

The solution to ln((6x)/(sqrt(x^2-4))) is ln(6)+ln(x)-ln(sqrt(x^2-4))

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simplify ln((6x)/(sqrt(x^2-4)))

simplify

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

ln (6) + ln (x) - ln (x^{2} - 4)

Solution steps

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

Apply log rule:

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

ln (\frac{6 x}{x ^{2} - 4}) = ln (6 x) - ln (x^{2} - 4)

= ln (6 x) - ln (x^{2} - 4)

Apply log rule:

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

ln (6 x) = ln (6) + ln (x)

= ln (6) + ln (x) - ln (x^{2} - 4)

lo g_{5} (4) + lo g_{5} (10)

lo g_{10} (18) - lo g_{10} (2)

- lo g_{10} (1.52 \cdot 1 0^{- 5})

5 ln (x - 6) - 4 ln (x)

lo g_{10} (18) - lo g_{10} (9)

What is ln((6x)/(sqrt(x^2-4))) ?
The solution to ln((6x)/(sqrt(x^2-4))) is ln(6)+ln(x)-ln(sqrt(x^2-4))