en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(x^5y^2z)

Solution

simplify

ln (x^{5} y^{2} z)

Solution

5 ln (x) + 2 ln (y) + ln (z)

Solution steps

ln (x^{5} y^{2} z)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Popular Examples

simplify 3ln(t^2)+ln(t)simplify

3 ln (t^{2}) + ln (t)

simplify 5log_{a}(x)+3log_{a}(y)simplify

5 lo g_{a} (x) + 3 lo g_{a} (y)

simplify ln(1/298)*4.87 simplify

ln (\frac{1}{298}) \cdot 4.87

simplify ln(118/1)simplify

ln (\frac{118}{1})

simplify ln(a*e^{b*x})simplify

ln (a \cdot e^{b \cdot x})

Frequently Asked Questions (FAQ)

What is ln(x^5y^2z) ?
The solution to ln(x^5y^2z) is 5ln(x)+2ln(y)+ln(z)