What is expand ln((e^x)/(sqrt(x)(x+3)^2)) ?

The solution to expand ln((e^x)/(sqrt(x)(x+3)^2)) is x-ln(sqrt(x))-2ln(x+3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand ln((e^x)/(sqrt(x)(x+3)^2))

expand

ln (\frac{e ^{x}}{x ( x + 3 ) ^{2}})

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

Solution steps

ln (\frac{e ^{x}}{x ( x + 3 ) ^{2}})

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{x}) = x ln (e)

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

x ln (e) = x

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

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

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

\frac{1}{2} ln (y) - \frac{1}{2} ln (y + 2)

4 ln (\frac{1}{4})

lo g_{6} (\frac{36 y}{x ^{7} z ^{3}})

ln (\frac{5}{x ^{2} + 9})

ln (\frac{575}{500})

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