What is ln(5)+1/2 ln(x+1)-2ln(1+sqrt(x)) ?

The solution to ln(5)+1/2 ln(x+1)-2ln(1+sqrt(x)) is ln((5(x+1)^{1/2})/((1+sqrt(x))^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(5)+1/2 ln(x+1)-2ln(1+sqrt(x))

simplify

ln (5) + \frac{1}{2} ln (x + 1) - 2 ln (1 + x)

ln (\frac{5 ( x + 1 ) ^{\frac{1}{2}}}{( 1 + x ) ^{2}})

Solution steps

ln (5) + \frac{1}{2} ln (x + 1) - 2 ln (1 + x)

Apply log rule:

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

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

= ln (5) + ln ((x + 1)^{\frac{1}{2}}) - 2 ln (x + 1)

Apply log rule:

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

ln (5) + ln ((x + 1)^{\frac{1}{2}}) = ln (5 (x + 1)^{\frac{1}{2}})

= ln (5 (x + 1)^{\frac{1}{2}}) - 2 ln (1 + x)

Apply log rule:

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

2 ln (x + 1) = ln ((x + 1)^{2})

= ln (5 (x + 1)^{\frac{1}{2}}) - ln ((x + 1)^{2})

Apply log rule:

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

ln (5 (x + 1)^{\frac{1}{2}}) - ln ((1 + x)^{2}) = ln (\frac{5 ( x + 1 ) ^{\frac{1}{2}}}{( x + 1 ) ^{2}})

= ln (\frac{5 ( x + 1 ) ^{\frac{1}{2}}}{( 1 + x ) ^{2}})

3 lo g_{5} (\frac{u v ^{2}}{w ^{3}})

\frac{1}{2} lo g_{10} (24) - lo g_{10} (4)

lo g_{b} (x^{3} \frac{y ^{2}}{z})

ln (\frac{4 x}{7 y ^{2}})

What is ln(5)+1/2 ln(x+1)-2ln(1+sqrt(x)) ?
The solution to ln(5)+1/2 ln(x+1)-2ln(1+sqrt(x)) is ln((5(x+1)^{1/2})/((1+sqrt(x))^2))