What is simplify-4ln(x)-2ln(y)-3ln(z) ?

The solution to simplify-4ln(x)-2ln(y)-3ln(z) is -ln(x^4y^2z^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-4ln(x)-2ln(y)-3ln(z)

simplify

- 4 ln (x) - 2 ln (y) - 3 ln (z)

- ln (x^{4} y^{2} z^{3})

Solution steps

- 4 ln (x) - 2 ln (y) - 3 ln (z)

Apply log rule:

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

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

= - ln (x^{4}) - 2 ln (y) - 3 ln (z)

Apply log rule:

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

2 ln (y) = ln (y^{2})

= - ln (x^{4}) - ln (y^{2}) - 3 ln (z)

Rewrite

- ln (x^{4}) - ln (y^{2})

- (ln (x^{4}) + ln (y^{2}))

= - (ln (x^{4}) + ln (y^{2})) - 3 ln (z)

Apply log rule:

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

ln (x^{4}) + ln (y^{2}) = ln (x^{4} y^{2})

= - ln (x^{4} y^{2}) - 3 ln (z)

Apply log rule:

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

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

= - ln (x^{4} y^{2}) - ln (z^{3})

Rewrite

- ln (x^{4} y^{2}) - ln (z^{3})

- (ln (x^{4} y^{2}) + ln (z^{3}))

= - (ln (z^{3}) + ln (x^{4} y^{2}))

Apply log rule:

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

ln (x^{4} y^{2}) + ln (z^{3}) = ln (x^{4} y^{2} z^{3})

= - ln (x^{4} y^{2} z^{3})

lo g_{5} (\frac{25 b ^{5} y ^{2} - 9}{y ( x + 9 ) ^{2}})

ln (7) + ln (4)

ln (\frac{83}{3})

lo g_{10} (3) 5

ln (7) + ln (2)

What is simplify-4ln(x)-2ln(y)-3ln(z) ?
The solution to simplify-4ln(x)-2ln(y)-3ln(z) is -ln(x^4y^2z^3)