What is e^{sqrt(x)}-ln(4e^{e^{sqrt(x)}}) ?

The solution to e^{sqrt(x)}-ln(4e^{e^{sqrt(x)}}) is -2ln(2)

Popular >

simplify e^{sqrt(x)}-ln(4e^{e^{sqrt(x)}})

simplify

e^{x} - ln (4 e^{e^{x}})

- 2 ln (2)

Decimal

- 1.38629 \dots

Solution steps

e^{x} - ln (4 e^{e^{x}})

Apply log rule:

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

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

= e^{x} - (ln (e^{e^{x}}) + ln (4))

Apply log rule:

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

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

= e^{x} - (ln (4) + e^{x} ln (e))

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

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

- (2 ln (2) + e^{x}) : - 2 ln (2) - e^{x}

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

Simplify

e^{x} - 2 ln (2) - e^{x} : - 2 ln (2)

= - 2 ln (2)

ln (10) - ln (5)

lo g_{b} (\frac{x ^{2} y}{z ^{6}})

lo g_{10} (\frac{y ^{7}}{x z ^{3}})

lo g_{10} (100 y)

lo g_{10} (0.1) - lo g_{10} (0.01)

What is e^{sqrt(x)}-ln(4e^{e^{sqrt(x)}}) ?
The solution to e^{sqrt(x)}-ln(4e^{e^{sqrt(x)}}) is -2ln(2)