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

The solution to simplify-3ln(x)-3ln(y)+3ln(z) is ln((z^3)/(x^3y^3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-3ln(x)-3ln(y)+3ln(z)

simplify

- 3 ln (x) - 3 ln (y) + 3 ln (z)

ln (\frac{z ^{3}}{x ^{3} y ^{3}})

Solution steps

- 3 ln (x) - 3 ln (y) + 3 ln (z)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Rewrite

- ln (x^{3}) - ln (y^{3})

- (ln (x^{3}) + ln (y^{3}))

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

Apply log rule:

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

ln (x^{3}) + ln (y^{3}) = ln (x^{3} y^{3})

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (z^{3}) - ln (x^{3} y^{3}) = ln (\frac{z ^{3}}{x ^{3} y ^{3}})

= ln (\frac{z ^{3}}{x ^{3} y ^{3}})

\frac{1}{3} ln (8) - ln (x) + 2 ln (x) y

- lo g_{10} (4.2 \cdot 1 0^{- 10})

- ln (x y)

ln (\frac{0.017}{0.01})

2 lo g_{10} (a) + lo g_{10} (b)

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