en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((2/3 x) 1/2 y)

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (\frac{2}{3} x) = ln (\frac{2}{3}) + ln (x)

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

Apply log rule:

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

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

= ln (2) - ln (3) + ln (x) + + ln (1) - ln (2) + ln (y)

Simplify

ln (2) - ln (3) + ln (x) + + ln (1) - ln (2) + ln (y) : - ln (3) + ln (1) + ln (x) + ln (y)

Apply log rule:

lo g_{a} (1) = 0

= - ln (3) + 0 + ln (x) + ln (y)

- ln (3) + 0 + ln (x) + ln (y) = - ln (3) + ln (x) + ln (y)

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

Popular Examples

simplify-9ln(t)+ln(6)-ln(6+1)simplify

- 9 ln (t) + ln (6) - ln (6 + 1)

simplify 1/3 log_{10}(x)-log_{10}(y)-2log_{10}(z)simplify

\frac{1}{3} lo g_{10} (x) - lo g_{10} (y) - 2 lo g_{10} (z)

simplify log_{2}(1/4)-log_{2}(sqrt(2)-x)simplify

lo g_{2} (\frac{1}{4}) - lo g_{2} (2 - x)

simplify 1/2+7log_{2}(x)-3/2 log_{2}(y)simplify

\frac{1}{2} + 7 lo g_{2} (x) - \frac{3}{2} lo g_{2} (y)

simplify log_{10}(pi)+2log_{10}(r)simplify

lo g_{10} (π) + 2 lo g_{10} (r)

Frequently Asked Questions (FAQ)

What is ln((2/3 x) 1/2 y) ?
The solution to ln((2/3 x) 1/2 y) is ln(x)+ln(y)-ln(3)