What is simplify-9ln(9x)-(1/9)ln(2700-9x) ?

The solution to simplify-9ln(9x)-(1/9)ln(2700-9x) is -ln(387420489x^9(2700-9x)^{1/9})

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simplify-9ln(9x)-(1/9)ln(2700-9x)

simplify

- 9 ln (9 x) - (\frac{1}{9}) ln (2700 - 9 x)

- ln (387420489 x^{9} (2700 - 9 x)^{\frac{1}{9}})

Solution steps

- 9 ln (9 x) - (\frac{1}{9}) ln (2700 - 9 x)

Apply log rule:

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

9 ln (9 x) = ln ((9 x)^{9})

= - ln ((9 x)^{9}) - (\frac{1}{9}) ln (- 9 x + 2700)

Apply log rule:

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

(\frac{1}{9}) ln (- 9 x + 2700) = ln ((- 9 x + 2700)^{(\frac{1}{9})})

= - ln ((9 x)^{9}) - ln ((- 9 x + 2700)^{(\frac{1}{9})})

Rewrite

- ln ((9 x)^{9}) - ln ((- 9 x + 2700)^{(\frac{1}{9})})

- (ln ((9 x)^{9}) + ln ((- 9 x + 2700)^{(\frac{1}{9})}))

= - (ln ((9 x)^{9}) + ln ((- 9 x + 2700)^{(\frac{1}{9})}))

Apply log rule:

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

ln ((9 x)^{9}) + ln ((2700 - 9 x)^{(\frac{1}{9})}) = ln ((9 x)^{9} (- 9 x + 2700)^{\frac{1}{9}})

= - ln ((9 x)^{9} (- 9 x + 2700)^{\frac{1}{9}})

Simplify

(9 x)^{9} (2700 - 9 x)^{(\frac{1}{9})} : 387420489 x^{9} (2700 - 9 x)^{\frac{1}{9}}

= - ln (387420489 x^{9} (2700 - 9 x)^{\frac{1}{9}})

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What is simplify-9ln(9x)-(1/9)ln(2700-9x) ?
The solution to simplify-9ln(9x)-(1/9)ln(2700-9x) is -ln(387420489x^9(2700-9x)^{1/9})