What is simplify-4ln(x)-5ln(y)-8ln(z) ?

The solution to simplify-4ln(x)-5ln(y)-8ln(z) is -ln(x^4y^5z^8)

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simplify-4ln(x)-5ln(y)-8ln(z)

simplify

- 4 ln (x) - 5 ln (y) - 8 ln (z)

- ln (x^{4} y^{5} z^{8})

Solution steps

- 4 ln (x) - 5 ln (y) - 8 ln (z)

Apply log rule:

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

4 ln (x) = ln (x^{4})

= - ln (x^{4}) - 5 ln (y) - 8 ln (z)

Apply log rule:

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

5 ln (y) = ln (y^{5})

= - ln (x^{4}) - ln (y^{5}) - 8 ln (z)

Rewrite

- ln (x^{4}) - ln (y^{5})

- (ln (x^{4}) + ln (y^{5}))

= - (ln (x^{4}) + ln (y^{5})) - 8 ln (z)

Apply log rule:

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

ln (x^{4}) + ln (y^{5}) = ln (x^{4} y^{5})

= - ln (x^{4} y^{5}) - 8 ln (z)

Apply log rule:

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

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

= - ln (x^{4} y^{5}) - ln (z^{8})

Rewrite

- ln (x^{4} y^{5}) - ln (z^{8})

- (ln (x^{4} y^{5}) + ln (z^{8}))

= - (ln (z^{8}) + ln (x^{4} y^{5}))

Apply log rule:

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

ln (x^{4} y^{5}) + ln (z^{8}) = ln (x^{4} y^{5} z^{8})

= - ln (x^{4} y^{5} z^{8})

2 ln (5) - ln (4)

ln (\frac{x}{x ^{2} + 9})

lo g_{5} (k^{2} - 25) - lo g_{5} (k) - 5

ln (9) + ln (4)

lo g_{10} (\frac{3 x}{2})

What is simplify-4ln(x)-5ln(y)-8ln(z) ?
The solution to simplify-4ln(x)-5ln(y)-8ln(z) is -ln(x^4y^5z^8)