en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(x^7y^9z)

Solution

simplify

ln (x^{7} y^{9} z)

Solution

7 ln (x) + 9 ln (y) + ln (z)

Solution steps

ln (x^{7} y^{9} z)

Apply log rule:

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

ln (x^{7} y^{9} z) = ln (x^{7}) + ln (y^{9}) + ln (z)

= ln (x^{7}) + ln (y^{9}) + ln (z)

Apply log rule:

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

ln (x^{7}) = 7 ln (x)

= 7 ln (x) + ln (y^{9}) + ln (z)

Apply log rule:

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

ln (y^{9}) = 9 ln (y)

= 7 ln (x) + 9 ln (y) + ln (z)

Popular Examples

simplify ln(y/(1000-y))simplify

ln (\frac{y}{1000 - y})

simplify ln(1/(2pis^2))simplify

ln (\frac{1}{2 π s ^{2}})

simplify log_{1/4}(3sqrt(32))simplify

lo g_{\frac{1}{4}} (332)

simplify 3log_{10}(X)+2log_{10}(y)simplify

3 lo g_{10} (X) + 2 lo g_{10} (y)

simplify ln(ae^{-kt})simplify

ln (a e^{- k t})

Frequently Asked Questions (FAQ)

What is ln(x^7y^9z) ?
The solution to ln(x^7y^9z) is 7ln(x)+9ln(y)+ln(z)