What is factor 4ln|x-2|+10ln|x+5| ?

The solution to factor 4ln|x-2|+10ln|x+5| is ln((x-2)^4(x+5)^{10})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor 4ln|x-2|+10ln|x+5|

factor

4 ln ∣ x - 2 ∣ + 10 ln ∣ x + 5 ∣

ln ((x - 2)^{4} (x + 5)^{10})

Solution steps

4 ln ∣ x - 2 ∣ + 10 ln ∣ x + 5 ∣

Apply log rule:

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

4 ln ∣ x - 2 ∣ = ln (∣ x - 2 ∣^{4})

= ln (∣ x - 2 ∣^{4}) + 10 ln ∣ x + 5 ∣

Apply log rule:

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

10 ln ∣ x + 5 ∣ = ln (∣ x + 5 ∣^{10})

= ln (∣ x - 2 ∣^{4}) + ln (∣ x + 5 ∣^{10})

Apply log rule:

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

ln (∣ x - 2 ∣^{4}) + ln (∣ x + 5 ∣^{10}) = ln (∣ x + 5 ∣^{10} ∣ x - 2 ∣^{4})

= ln (∣ x + 5 ∣^{10} ∣ x - 2 ∣^{4})

Factor

∣ x - 2 ∣^{4} ∣ x + 5 ∣^{10} : (x - 2)^{4} (x + 5)^{10}

= ln ((x - 2)^{4} (x + 5)^{10})

6 lo g_{3} (u) + 4 lo g_{3} (v)

ln (y) + ln (cos (v))

ln (56) - ln (8)

ln ∣ x ∣ + \frac{1}{2} ln ∣ x + 2 ∣ - \frac{1}{3} ln ∣ x - 3 ∣

ln (\frac{m}{8} (p - 9))

What is factor 4ln|x-2|+10ln|x+5| ?
The solution to factor 4ln|x-2|+10ln|x+5| is ln((x-2)^4(x+5)^{10})