en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify e^{2ln|ln(x)|+ln(x)}

Solution

simplify

e^{2 l n ∣ l n (x) ∣ + l n (x)}

Solution

x ln^{2} (x)

Solution steps

e^{2 l n ∣ l n (x) ∣ + l n (x)}

Apply log rule:

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

2 ln ∣ ln (x) ∣ = ln (∣ ln (x) ∣^{2})

= e^{l n (∣ l n (x) ∣^{2}) + l n (x)}

Apply log rule:

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

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

= e^{l n (∣ l n (x) ∣^{2} x)}

∣ ln (x) ∣^{2} = ln^{2} (x)

= e^{l n (x l n^{2} (x))}

Apply log rule:

a^{l o g_{a} (b)} = b

= x ln^{2} (x)

Popular Examples

simplify log_{10}(1.2e^{-3})simplify

lo g_{10} (1.2 e^{- 3})

simplify ln(Ae^{3/2 t^2})simplify

ln (A e^{\frac{3}{2} t^{2}})

simplify ln|4|+2ln(4^2+4)-ln|1|+2ln(1^2+4)simplify

ln ∣ 4 ∣ + 2 ln (4^{2} + 4) - ln ∣ 1 ∣ + 2 ln (1^{2} + 4)

simplify ln((3sqrt(5))/(\sqrt[3]{7)})simplify

simplify ln(w)+6ln(u)-2ln(v)simplify

ln (w) + 6 ln (u) - 2 ln (v)

Frequently Asked Questions (FAQ)

What is e^{2ln|ln(x)|+ln(x)} ?
The solution to e^{2ln|ln(x)|+ln(x)} is xln^2(x)