en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand ln((3x^5)/y)

Solution

expand

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (3 x^{5}) = ln (3) + ln (x^{5})

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

Apply log rule:

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

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

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

Popular Examples

simplify ln(8c)simplify

ln (8 c)

simplify ln((1+x^2)/(1-x^2))simplify

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

simplify 1/180 (ln|180x-30|-ln(30))simplify

\frac{1}{180} (ln ∣ 180 x - 30 ∣ - ln (30))

simplify-log_{10}(6*10^{-3})simplify

- lo g_{10} (6 \cdot 1 0^{- 3})

simplify 3ln(4)-1/2 ln(x^2+4)simplify

3 ln (4) - \frac{1}{2} ln (x^{2} + 4)

Frequently Asked Questions (FAQ)

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