What is 2ln(2)-1/2 ln(x^3+4x) ?

The solution to 2ln(2)-1/2 ln(x^3+4x) is ln((4sqrt(x^3+4x))/(x^3+4x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(2)-1/2 ln(x^3+4x)

simplify

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

ln (\frac{4 x ^{3} + 4 x}{x ^{3} + 4 x})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

\frac{1}{2} ln (x^{3} + 4 x) = ln ((x^{3} + 4 x)^{\frac{1}{2}})

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

Apply log rule:

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

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

= ln (\frac{2 ^{2}}{( x ^{3} + 4 x ) ^{\frac{1}{2}}})

Simplify

\frac{2 ^{2}}{( x ^{3} + 4 x ) ^{\frac{1}{2}}} : \frac{4 x ^{3} + 4 x}{x ^{3} + 4 x}

= ln (\frac{4 x ^{3} + 4 x}{x ^{3} + 4 x})

lo g_{9} (\frac{z}{81})

lo g_{5} ((u v^{5})^{2})

4 lo g_{3} (x) - 4 lo g_{3} (y)

lo g_{a} (4 a)

What is 2ln(2)-1/2 ln(x^3+4x) ?
The solution to 2ln(2)-1/2 ln(x^3+4x) is ln((4sqrt(x^3+4x))/(x^3+4x))