What is expand ln((x^4sqrt(y))/(3z^5)) ?

The solution to expand ln((x^4sqrt(y))/(3z^5)) is 4ln(x)+ln(sqrt(y))-ln(3)-5ln(z)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand ln((x^4sqrt(y))/(3z^5))

expand

ln (\frac{x ^{4} y}{3 z ^{5}})

4 ln (x) + ln (y) - ln (3) - 5 ln (z)

Solution steps

ln (\frac{x ^{4} y}{3 z ^{5}})

Apply log rule:

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

ln (\frac{x ^{4} y}{3 z ^{5}}) = ln (x^{4} y) - ln (3 z^{5})

= ln (x^{4} y) - ln (3 z^{5})

Apply log rule:

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

ln (x^{4} y) = ln (x^{4}) + ln (y), ln (3 z^{5}) = ln (3) + ln (z^{5})

= ln (x^{4}) + ln (y) - (ln (z^{5}) + ln (3))

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) - (ln (3) + 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) + ln (y) - (ln (3) + 5 ln (z))

- (ln (3) + 5 ln (z)) : - ln (3) - 5 ln (z)

= 4 ln (x) + ln (y) - ln (3) - 5 ln (z)

ln (x^{3} 2 - x)

3 lo g_{10} (x) - 6 lo g_{10} (x + 1)

ln (4) + 2 ln (x) + 3 ln (x^{2} + 3)

7 lo g_{3} (a) + 2 lo g_{3} (b) - \frac{1}{2} lo g_{3} (2 c)

lo g_{10} (a) - 2 lo g_{10} (b) + 3 lo g_{10} (c)

What is expand ln((x^4sqrt(y))/(3z^5)) ?
The solution to expand ln((x^4sqrt(y))/(3z^5)) is 4ln(x)+ln(sqrt(y))-ln(3)-5ln(z)