en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(x)-x/θ-2ln(θ)

Solution

simplify

ln (x) - \frac{x}{θ} - 2 ln (θ)

Solution

ln (\frac{x}{θ ^{2}}) - \frac{x}{θ}

Solution steps

ln (x) - \frac{x}{θ} - 2 ln (θ)

Apply log rule:

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

2 ln (θ) = ln (θ^{2})

= ln (x) - \frac{x}{θ} - ln (θ^{2})

Apply log rule:

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

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

= ln (\frac{x}{θ ^{2}}) - \frac{x}{θ}

Popular Examples

simplify-7/12 log_{2}(7/12)-5/12 log_{2}(5/12)simplify

- \frac{7}{12} lo g_{2} (\frac{7}{12}) - \frac{5}{12} lo g_{2} (\frac{5}{12})

expand ln(x^5y^3)expand

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

simplify log_{10}(x/(y^4\sqrt[3]{z^2)})simplify

simplify log_{10}(x/(2y))simplify

lo g_{10} (\frac{x}{2 y})

simplify log_{10}((-11^7)/(-11^35^8))simplify

lo g_{10} (\frac{- 1 1 ^{7}}{- 1 1 ^{3} 5 ^{8}})

Frequently Asked Questions (FAQ)

What is ln(x)-x/θ-2ln(θ) ?
The solution to ln(x)-x/θ-2ln(θ) is ln(x/(θ^2))-x/θ