What is expand-7ln(x)-8ln(y)-3ln(z) ?

The solution to expand-7ln(x)-8ln(y)-3ln(z) is -ln(x^7y^8z^3)

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expand-7ln(x)-8ln(y)-3ln(z)

expand

- 7 ln (x) - 8 ln (y) - 3 ln (z)

- ln (x^{7} y^{8} z^{3})

Solution steps

- 7 ln (x) - 8 ln (y) - 3 ln (z)

Apply log rule:

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

7 ln (x) = ln (x^{7})

= - ln (x^{7}) - 8 ln (y) - 3 ln (z)

Apply log rule:

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

8 ln (y) = ln (y^{8})

= - ln (x^{7}) - ln (y^{8}) - 3 ln (z)

Rewrite

- ln (x^{7}) - ln (y^{8})

- (ln (x^{7}) + ln (y^{8}))

= - (ln (x^{7}) + ln (y^{8})) - 3 ln (z)

Apply log rule:

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

ln (x^{7}) + ln (y^{8}) = ln (x^{7} y^{8})

= - ln (x^{7} y^{8}) - 3 ln (z)

Apply log rule:

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

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

= - ln (x^{7} y^{8}) - ln (z^{3})

Rewrite

- ln (x^{7} y^{8}) - ln (z^{3})

- (ln (x^{7} y^{8}) + ln (z^{3}))

= - (ln (z^{3}) + ln (x^{7} y^{8}))

Apply log rule:

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

ln (x^{7} y^{8}) + ln (z^{3}) = ln (x^{7} y^{8} z^{3})

= - ln (x^{7} y^{8} z^{3})

ln (\frac{2}{15})

- 3 (\frac{1}{2} ln (2^{2} - 9) - \frac{1}{2} ln (- 2^{2} - 9))

lo g_{b} (\frac{1}{10}) + lo g_{b} (30)

2.715096 - 1.70203 - 0.287 ln (\frac{3000}{110})

lo g_{3} (u) - 5 lo g_{3} (v)

What is expand-7ln(x)-8ln(y)-3ln(z) ?
The solution to expand-7ln(x)-8ln(y)-3ln(z) is -ln(x^7y^8z^3)