What is 1/2 ln|2(10.3)+1|+2ln|(10.3)-1| ?

The solution to 1/2 ln|2(10.3)+1|+2ln|(10.3)-1| is ln(401.96919…)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/2 ln|2(10.3)+1|+2ln|(10.3)-1|

simplify

\frac{1}{2} ln ∣ 2 (10.3) + 1 ∣ + 2 ln ∣ (10.3) - 1 ∣

ln (401.96919 \dots)

Decimal Notation

5.99637 \dots

Solution steps

\frac{1}{2} ln ∣ 2 (10.3) + 1 ∣ + 2 ln ∣ (10.3) - 1 ∣

Apply log rule:

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

\frac{1}{2} ln ∣ 2 (10.3) + 1 ∣ = ln (∣ 2 (10.3) + 1 ∣^{\frac{1}{2}})

= ln (∣ 2 (10.3) + 1 ∣^{\frac{1}{2}}) + 2 ln ∣ (10.3) - 1 ∣

Apply log rule:

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

2 ln ∣ (10.3) - 1 ∣ = ln (∣ (10.3) - 1 ∣^{2})

= ln (∣ 2 (10.3) + 1 ∣^{\frac{1}{2}}) + ln (∣ (10.3) - 1 ∣^{2})

Apply log rule:

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

ln (∣ 2 (10.3) + 1 ∣^{\frac{1}{2}}) + ln (∣ (10.3) - 1 ∣^{2}) = ln (∣ 10.3 - 1 ∣^{2} ∣ 2 \cdot 10.3 + 1 ∣^{\frac{1}{2}})

= ln (∣ 10.3 - 1 ∣^{2} ∣ 2 \cdot 10.3 + 1 ∣^{\frac{1}{2}})

∣ 2 (10.3) + 1 ∣^{\frac{1}{2}} ∣ (10.3) - 1 ∣^{2} = 401.96919 \dots

= ln (401.96919 \dots)

\frac{1}{4} ln (\frac{3 e ^{\frac{3}{2} x}}{3 e ^{\frac{3}{2} x} - 2})

ln (\frac{2.3}{2.6})

\frac{1}{2} [ln (x + 1) + 2 ln (x - 1)] + 3 ln (x)

- 0.3 lo g_{2} (0.3) - 0.7 lo g_{2} (0.7)

ln (Y \cdot e^{- a (i)})

What is 1/2 ln|2(10.3)+1|+2ln|(10.3)-1| ?
The solution to 1/2 ln|2(10.3)+1|+2ln|(10.3)-1| is ln(401.96919…)