What is 2ln(x+2)-ln(x+2)-ln(2)3 ?

The solution to 2ln(x+2)-ln(x+2)-ln(2)3 is ln((x+2)/8)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(x+2)-ln(x+2)-ln(2)3

simplify

2 ln (x + 2) - ln (x + 2) - ln (2) 3

ln (\frac{x + 2}{8})

Solution steps

2 ln (x + 2) - ln (x + 2) - ln (2) \cdot 3

Apply log rule:

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

3 ln (2) = ln (2^{3})

= 2 ln (x + 2) - ln (x + 2) - ln (2^{3})

Rewrite

- ln (x + 2) - ln (2^{3})

- (ln (x + 2) + ln (2^{3}))

= 2 ln (x + 2) - (ln (x + 2) + ln (2^{3}))

Apply log rule:

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

ln (x + 2) + ln (2^{3}) = ln (2^{3} (x + 2))

= 2 ln (x + 2) - ln (2^{3} (x + 2))

2^{3} = 8

= 2 ln (x + 2) - ln (8 (x + 2))

Apply log rule:

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

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

= ln ((x + 2)^{2}) - ln (8 (x + 2))

Apply log rule:

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

ln ((x + 2)^{2}) - ln (8 (x + 2)) = ln (\frac{( x + 2 ) ^{2}}{8 ( x + 2 )})

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

Cancel the common factor:

x + 2

= ln (\frac{x + 2}{8})

ln (2^{x} (2 - x)^{5})

- ln (\frac{3}{2})

ln ∣ y ∣ - ln ∣ y - 1 ∣

- 0.2 \cdot lo g_{2} (0.2) - 0.8 \cdot lo g_{2} (0.8)

ln (\frac{k}{2 k})

What is 2ln(x+2)-ln(x+2)-ln(2)3 ?
The solution to 2ln(x+2)-ln(x+2)-ln(2)3 is ln((x+2)/8)