en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(x)+2ln(y)-ln(z)

Solution

simplify

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

Solution

ln (\frac{x y ^{2}}{z})

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

= ln (x y^{2}) - ln (z)

Apply log rule:

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

ln (x y^{2}) - ln (z) = ln (\frac{x y ^{2}}{z})

= ln (\frac{x y ^{2}}{z})

Popular Examples

expand log_{2}(16x^2w^8\sqrt[3]{y})expand

simplify-2ln(3)+2ln(2)simplify

- 2 ln (3) + 2 ln (2)

simplify ln(3x)-ln(2x)simplify

ln (3 x) - ln (2 x)

simplify ln(10)-ln(3)simplify

ln (10) - ln (3)

simplify log_{a}(25/27)simplify

lo g_{a} (\frac{25}{27})

Frequently Asked Questions (FAQ)

What is ln(x)+2ln(y)-ln(z) ?
The solution to ln(x)+2ln(y)-ln(z) is ln((xy^2)/z)