What is 1/9 ln(x-15)-1/9 ln(x-6) ?

The solution to 1/9 ln(x-15)-1/9 ln(x-6) is ln(\sqrt[9]{(x-15)/(x-6)})

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simplify 1/9 ln(x-15)-1/9 ln(x-6)

simplify

\frac{1}{9} ln (x - 15) - \frac{1}{9} ln (x - 6)

Solution steps

\frac{1}{9} ln (x - 15) - \frac{1}{9} ln (x - 6)

Apply log rule:

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

\frac{1}{9} ln (x - 15) = ln ((x - 15)^{\frac{1}{9}})

= ln ((x - 15)^{\frac{1}{9}}) - \frac{1}{9} ln (x - 6)

Apply log rule:

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

\frac{1}{9} ln (x - 6) = ln ((x - 6)^{\frac{1}{9}})

= ln ((x - 15)^{\frac{1}{9}}) - ln ((x - 6)^{\frac{1}{9}})

Apply log rule:

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

ln ((x - 15)^{\frac{1}{9}}) - ln ((x - 6)^{\frac{1}{9}}) = ln (\frac{( x - 15 ) ^{\frac{1}{9}}}{( x - 6 ) ^{\frac{1}{9}}})

= ln (\frac{( x - 15 ) ^{\frac{1}{9}}}{( x - 6 ) ^{\frac{1}{9}}})

Combine same powers :

t, s t + 1 = t^{2} + s

z^{2} = 4 + 4 r^{2}

(1 - 2 x) (1 - 3 x) = (5 x - 1) x - 2 (2 x - 5)

2 x^{2} + 16 x - 96 = 0

- 10 t^{2} - 12 t = - 9982

What is 1/9 ln(x-15)-1/9 ln(x-6) ?
The solution to 1/9 ln(x-15)-1/9 ln(x-6) is ln(\sqrt[9]{(x-15)/(x-6)})