What is 30-12ln(x)-18ln(y) ?

The solution to 30-12ln(x)-18ln(y) is 30-ln(x^{12}y^{18})

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simplify 30-12ln(x)-18ln(y)

simplify

30 - 12 ln (x) - 18 ln (y)

30 - ln (x^{12} y^{18})

Solution steps

30 - 12 ln (x) - 18 ln (y)

Apply log rule:

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

12 ln (x) = ln (x^{12})

= 30 - ln (x^{12}) - 18 ln (y)

Apply log rule:

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

18 ln (y) = ln (y^{18})

= 30 - ln (x^{12}) - ln (y^{18})

Rewrite

- ln (x^{12}) - ln (y^{18})

- (ln (x^{12}) + ln (y^{18}))

= 30 - (ln (x^{12}) + ln (y^{18}))

Apply log rule:

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

ln (x^{12}) + ln (y^{18}) = ln (x^{12} y^{18})

= 30 - ln (x^{12} y^{18})

lo g_{4} (\frac{m}{n})

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3 ln (3 x)

ln (3 (10 x^{2})^{x})

ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣

What is 30-12ln(x)-18ln(y) ?
The solution to 30-12ln(x)-18ln(y) is 30-ln(x^{12}y^{18})