What is ln((x^4)/(y^2z^5)) ?

The solution to ln((x^4)/(y^2z^5)) is 4ln(x)-2ln(y)-5ln(z)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((x^4)/(y^2z^5))

simplify

ln (\frac{x ^{4}}{y ^{2} z ^{5}})

4 ln (x) - 2 ln (y) - 5 ln (z)

Solution steps

ln (\frac{x ^{4}}{y ^{2} z ^{5}})

Apply log rule:

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

ln (\frac{x ^{4}}{y ^{2} z ^{5}}) = ln (x^{4}) - ln (y^{2} z^{5})

= ln (x^{4}) - ln (y^{2} z^{5})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 4 ln (x) - ln (y^{2} z^{5})

Apply log rule:

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

ln (y^{2} z^{5}) = ln (y^{2}) + ln (z^{5})

= 4 ln (x) - (ln (y^{2}) + ln (z^{5}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 4 ln (x) - (2 ln (y) + ln (z^{5}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 4 ln (x) - (2 ln (y) + 5 ln (z))

- (2 ln (y) + 5 ln (z)) : - 2 ln (y) - 5 ln (z)

= 4 ln (x) - 2 ln (y) - 5 ln (z)

\frac{ln ( 330 ) - ln ( 166 )}{7}

- lo g_{10} (3.4 x 1 0^{- 4})

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

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

ln (A B)

What is ln((x^4)/(y^2z^5)) ?
The solution to ln((x^4)/(y^2z^5)) is 4ln(x)-2ln(y)-5ln(z)