What is ln((2x^2+6x+6)/(x^{6/5)cos(x)}) ?

The solution to ln((2x^2+6x+6)/(x^{6/5)cos(x)}) is ln(2x^2+6x+6)-6/5 ln(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((2x^2+6x+6)/(x^{6/5)cos(x)})

simplify

ln (\frac{2 x ^{2} + 6 x + 6}{x ^{\frac{6}{5}} cos ( x )})

ln (2 x^{2} + 6 x + 6) - \frac{6}{5} ln (x) - ln (cos (x))

Solution steps

ln (\frac{2 x ^{2} + 6 x + 6}{x ^{\frac{6}{5}} cos ( x )})

Apply log rule:

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

ln (\frac{2 x ^{2} + 6 x + 6}{x ^{\frac{6}{5}} cos ( x )}) = ln (2 x^{2} + 6 x + 6) - ln (x^{\frac{6}{5}} cos (x))

= ln (2 x^{2} + 6 x + 6) - ln (x^{\frac{6}{5}} cos (x))

Apply log rule:

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

ln (x^{\frac{6}{5}} cos (x)) = ln (x^{\frac{6}{5}}) + ln (cos (x))

= ln (2 x^{2} + 6 x + 6) - (ln (x^{\frac{6}{5}}) + ln (cos (x)))

Apply log rule:

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

ln (x^{\frac{6}{5}}) = \frac{6}{5} ln (x)

= ln (2 x^{2} + 6 x + 6) - (\frac{6}{5} ln (x) + ln (cos (x)))

- (\frac{6}{5} ln (x) + ln (cos (x))) : - \frac{6}{5} ln (x) - ln (cos (x))

= ln (2 x^{2} + 6 x + 6) - \frac{6}{5} ln (x) - ln (cos (x))

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

\frac{1}{3} ln (\frac{2}{5})

3 lo g_{0.4} (2) - 3 lo g_{0.4} (5)

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

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

What is ln((2x^2+6x+6)/(x^{6/5)cos(x)}) ?
The solution to ln((2x^2+6x+6)/(x^{6/5)cos(x)}) is ln(2x^2+6x+6)-6/5 ln(x)-ln(cos(x))