What is 3ln(x)-ln(x+6)-ln(x-6) ?

The solution to 3ln(x)-ln(x+6)-ln(x-6) is ln((x^3)/((x+6)(x-6)))

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simplify 3ln(x)-ln(x+6)-ln(x-6)

simplify

3 ln (x) - ln (x + 6) - ln (x - 6)

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

Solution steps

3 ln (x) - ln (x + 6) - ln (x - 6)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (x) = ln (x^{3})

= ln (x^{3}) - ln (x + 6) - ln (x - 6)

Apply log rule:

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

ln (x^{3}) - ln (x + 6) = ln (\frac{x ^{3}}{x + 6})

= ln (\frac{x ^{3}}{x + 6}) - ln (x - 6)

Apply log rule:

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

ln (\frac{x ^{3}}{x + 6}) - ln (x - 6) = ln (\frac{\frac{x ^{3}}{x + 6}}{x - 6})

= ln (\frac{\frac{x ^{3}}{x + 6}}{x - 6})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{x ^{3}}{( x + 6 ) ( x - 6 )})

ln (\frac{R}{0.203})

5 ln (x) + 2 ln (y) + ln (z)

ln (\frac{100}{10})

lo g_{4} (\frac{3 x ^{2}}{y ^{3}})

ln (\frac{( x y ^{4} )}{z ^{3}})

What is 3ln(x)-ln(x+6)-ln(x-6) ?
The solution to 3ln(x)-ln(x+6)-ln(x-6) is ln((x^3)/((x+6)(x-6)))