What is 10-12ln(x)-18ln(y) ?

The solution to 10-12ln(x)-18ln(y) is 10-ln(x^{12}y^{18})

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simplify 10-12ln(x)-18ln(y)

simplify

10 - 12 ln (x) - 18 ln (y)

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

Solution steps

10 - 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})

= 10 - 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})

= 10 - ln (x^{12}) - ln (y^{18})

Rewrite

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

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

= 10 - (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})

= 10 - ln (x^{12} y^{18})

lo g_{2} (\frac{1}{12})

4 ln (x) - ln (x + 1)

- \frac{1}{32} ln ∣ x + 2 ∣ + \frac{1}{32} ln ∣ x - 2 ∣

ln (\frac{( 3 y + 1 ) ^{5}}{y ^{2} + 1})

ln (b) + \frac{ln ( c )}{2} - 3 ln (d)

What is 10-12ln(x)-18ln(y) ?
The solution to 10-12ln(x)-18ln(y) is 10-ln(x^{12}y^{18})