What is ln((((tan(x))^5))/(e^{2x^4)x^6}) ?

The solution to ln((((tan(x))^5))/(e^{2x^4)x^6}) is 5ln(tan(x))-2x^4-6ln(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((((tan(x))^5))/(e^{2x^4)x^6})

simplify

ln \frac{( ( tan ( x ) ) ^{5} )}{e ^{2 x^{4}} x ^{6}}

5 ln (tan (x)) - 2 x^{4} - 6 ln (x)

Solution steps

ln \frac{( ( tan ( x ) ) ^{5} )}{e ^{2 x^{4}} x ^{6}}

Apply log rule:

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

ln (\frac{( tan ^{5} ( x ) )}{e ^{2 x^{4}} x ^{6}}) = ln ((tan^{5} (x))) - ln (e^{2 x^{4}} x^{6})

= ln (tan^{5} (x)) - ln (e^{2 x^{4}} x^{6})

Apply log rule:

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

ln (tan^{5} (x)) = 5 ln (tan (x))

= 5 ln (tan (x)) - ln (e^{2 x^{4}} x^{6})

Apply log rule:

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

ln (e^{2 x^{4}} x^{6}) = ln (e^{2 x^{4}}) + ln (x^{6})

= 5 ln (tan (x)) - (ln (e^{2 x^{4}}) + ln (x^{6}))

Apply log rule:

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

ln (e^{2 x^{4}}) = 2 x^{4} ln (e)

= 5 ln (tan (x)) - (2 x^{4} ln (e) + ln (x^{6}))

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

= 5 ln (tan (x)) - (2 x^{4} ln (e) + 6 ln (x))

2 x^{4} ln (e) = 2 x^{4}

= 5 ln (tan (x)) - (2 x^{4} + 6 ln (x))

- (2 x^{4} + 6 ln (x)) : - 2 x^{4} - 6 ln (x)

= 5 ln (tan (x)) - 2 x^{4} - 6 ln (x)

- lo g_{10} (5.3 \cdot 1 0^{- 13})

ln (2.4 e^{- 7})

lo g_{7} ((a b^{6})^{5})

ln (\frac{4 x ^{2} + 5 x + 4}{x ^{\frac{5}{6}} tan ( x )})

ln (6) + ln (\frac{e ^{(1.24245)}}{3})

What is ln((((tan(x))^5))/(e^{2x^4)x^6}) ?
The solution to ln((((tan(x))^5))/(e^{2x^4)x^6}) is 5ln(tan(x))-2x^4-6ln(x)