What is simplify-12(1/2 ln|4x+10|-1/2 ln|4x+8|) ?

The solution to simplify-12(1/2 ln|4x+10|-1/2 ln|4x+8|) is -12ln(sqrt((|4x+10|)/(|4x+8|)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-12(1/2 ln|4x+10|-1/2 ln|4x+8|)

simplify

- 12 (\frac{1}{2} ln ∣ 4 x + 10 ∣ - \frac{1}{2} ln ∣ 4 x + 8 ∣)

- 12 ln (\frac{∣ 4 x + 10 ∣}{∣ 4 x + 8 ∣})

Solution steps

- 12 (\frac{1}{2} ln ∣ 4 x + 10 ∣ - \frac{1}{2} ln ∣ 4 x + 8 ∣)

Apply log rule:

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

\frac{1}{2} ln ∣ 4 x + 10 ∣ = ln (∣ 4 x + 10 ∣^{\frac{1}{2}})

= - 12 (ln (∣ 4 x + 10 ∣^{\frac{1}{2}}) - \frac{1}{2} ln ∣ 4 x + 8 ∣)

Apply log rule:

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

\frac{1}{2} ln ∣ 4 x + 8 ∣ = ln (∣ 4 x + 8 ∣^{\frac{1}{2}})

= - 12 (ln (∣ 4 x + 10 ∣^{\frac{1}{2}}) - ln (∣ 4 x + 8 ∣^{\frac{1}{2}}))

Apply log rule:

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

ln (∣ 4 x + 10 ∣^{\frac{1}{2}}) - ln (∣ 4 x + 8 ∣^{\frac{1}{2}}) = ln (\frac{∣ 4 x + 10 ∣ ^{\frac{1}{2}}}{∣ 4 x + 8 ∣ ^{\frac{1}{2}}})

= - 12 ln (\frac{∣ 4 x + 10 ∣ ^{\frac{1}{2}}}{∣ 4 x + 8 ∣ ^{\frac{1}{2}}})

Combine same powers :

= - 12 ln (\frac{∣ 4 x + 10 ∣}{∣ 4 x + 8 ∣})

ln (n (θ + 1))

ln (2 t^{2})

2 ln (8) - 2 ln (3)

7 ln (x - 2) + 7 ln (x + 2)

- lo g_{10} (2.34 \cdot 1 0^{- 7})

What is simplify-12(1/2 ln|4x+10|-1/2 ln|4x+8|) ?
The solution to simplify-12(1/2 ln|4x+10|-1/2 ln|4x+8|) is -12ln(sqrt((|4x+10|)/(|4x+8|)))