What is ln((6x)/(sqrt(x^2-9))) ?

The solution to ln((6x)/(sqrt(x^2-9))) is ln(6)+ln(x)-ln(sqrt(x^2-9))

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simplify ln((6x)/(sqrt(x^2-9)))

simplify

ln (\frac{6 x}{x ^{2} - 9})

ln (6) + ln (x) - ln (x^{2} - 9)

Solution steps

ln (\frac{6 x}{x ^{2} - 9})

Apply log rule:

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

ln (\frac{6 x}{x ^{2} - 9}) = ln (6 x) - ln (x^{2} - 9)

= ln (6 x) - ln (x^{2} - 9)

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} - 9)

lo g_{4} (19 b^{6} c)

ln (\frac{e ^{7}}{15})

lo g_{10} (x^{2}) - lo g_{10} (10 x)

lo g_{5} (\frac{x ^{4}}{25 y ^{2} z})

2 lo g_{7} (3 x) + 3 lo g_{7} (2 x)

What is ln((6x)/(sqrt(x^2-9))) ?
The solution to ln((6x)/(sqrt(x^2-9))) is ln(6)+ln(x)-ln(sqrt(x^2-9))