What is ln((x^2)/(e^{sqrt(x))cos(x)}) ?

The solution to ln((x^2)/(e^{sqrt(x))cos(x)}) is 2ln(x)-sqrt(x)-ln(cos(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((x^2)/(e^{sqrt(x))cos(x)})

simplify

ln (\frac{x ^{2}}{e ^{x} cos ( x )})

2 ln (x) - x - ln (cos (x))

Solution steps

ln (\frac{x ^{2}}{e ^{x} cos ( x )})

Apply log rule:

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

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

= ln (x^{2}) - ln (e^{x} cos (x))

Apply log rule:

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

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

= 2 ln (x) - ln (e^{x} cos (x))

Apply log rule:

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

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

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

Apply log rule:

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

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

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

x ln (e) = x

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

- (x + ln (cos (x))) : - x - ln (cos (x))

= 2 ln (x) - x - ln (cos (x))

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

- lo g_{10} (2 \cdot 1 0^{- 8})

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

5 ln (x y) - 3 ln (x z)

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

What is ln((x^2)/(e^{sqrt(x))cos(x)}) ?
The solution to ln((x^2)/(e^{sqrt(x))cos(x)}) is 2ln(x)-sqrt(x)-ln(cos(x))