What is ln((sqrt(x+9))/(x(x-4))) ?

The solution to ln((sqrt(x+9))/(x(x-4))) is ln(sqrt(x+9))-ln(x)-ln(x-4)

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simplify ln((sqrt(x+9))/(x(x-4)))

simplify

ln (\frac{x + 9}{x ( x - 4 )})

ln (x + 9) - ln (x) - ln (x - 4)

Solution steps

ln (\frac{x + 9}{x ( x - 4 )})

Apply log rule:

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

ln (\frac{x + 9}{x ( x - 4 )}) = ln (x + 9) - ln (x (x - 4))

= ln (x + 9) - ln (x (x - 4))

Apply log rule:

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

ln (x (x - 4)) = ln (x) + ln (x - 4)

= ln (x + 9) - (ln (x) + ln (x - 4))

- (ln (x) + ln (x - 4)) : - ln (x) - ln (x - 4)

= ln (x + 9) - ln (x) - ln (x - 4)

ln (3) + \frac{1}{2} ln (x) + ln (y) - \frac{1}{3} ln (z)

lo g_{10} (2) + lo g_{10} (9)

6 lo g_{10} (a) + lo g_{10} (b)

10 lo g_{10} (x) + \frac{2}{3} lo g_{10} (64)

\frac{1}{2} ln (x) + 5 ln (y) - 2 ln (z)

What is ln((sqrt(x+9))/(x(x-4))) ?
The solution to ln((sqrt(x+9))/(x(x-4))) is ln(sqrt(x+9))-ln(x)-ln(x-4)