Exam 4: Logarithm Functions

Find the values of x at which the function f(x) = $e ^ { - 2 x }$ + 2x has a possible relative maximum or minimum point.

2 ln(x + 1) - ln $x ^ { 2 }$ = 8 Enter your answer exactly as just $\frac { a } { e ^ { b } - c }$ .

ln xyz - ln $\left( \frac { y ^ { 2 } } { x } \right)$ Enter your answer as just ln $\frac { a ^ { n } b } { c }$ .

f(x) = $( \ln x ) ^ { 4 }$ Enter your answer as just $\frac { P ( \ln x ) } { Q ( x ) }$ where P is a polynomial in lnx and Q is a polynomial in x.

Which of the following functions y = f(x) satisfy y' = - $\frac { 2 } { 3 }$ y, f(1) = 1? (I) y = $e ^ { x }$ (II) y = $e ^ { - 2 / 3 x }$ (III) y = $\mathrm { e } ^ { ( - 2 / 3 ) ( x - 1 ) }$ (IV) y = - $\frac { 2 } { 3 }$ $e ^ { x }$

f(x) = $e ^ { x }$ + $\mathrm { e } ^ { 2 x }$ + $\frac { 1 } { e ^ { - 4 x } }$ Enter your answer exactly as just P( $e ^ { x }$ ) where P is a polynomial in $e ^ { x }$ in standard form.

Simplify - $4 ^ { x }$ ∙ $2 ^{x / 2}$ Enter your answer exactly as $2^{ \mathrm {~b} / \mathrm { c }}$ .

$\frac { \ln x } { x ^ { 3 } }$ Enter your answer exactly as just $\frac { a \pm b \ln c } { P ( x ) }$ where P is a polynomial in x in standard form.

$e ^ { 2 } \ln x$ Enter just a standard polynomial in x.

Find the slope of the tangent line to the curve (x + $\mathrm { e } ^ { - \mathrm { x } }$ $)^2$ at (0, 1). Enter just an integer.

Determine a function y = f(x) such that y' = $\frac { 1 } { 10 }$ y and f(0) = -3?

Simplify -ln $\frac { x ^ { 4 } - 5 } { z ^ { 3 } y ^ { 4 } }$

Solve for x. -2 ln x + ln $\frac { 1 } { x }$ = 3

2 $e ^ { x + 1 }$ + 2 = 6 Enter your answer exactly as just a ± ln b.

At what value of x could the function f(x) = $\frac { \ln x + x } { x }$ have a possible relative maximum or minimum?

$e ^ { x }$ ln 2x , Enter your answer exactly as $e ^ { a } \ln b \pm \frac { e ^ { \mathcal { C } } } { d }$

Solve for x. -3 + ln x = 0

Solve for x. - $e ^ { 1 + x ^ { 2 } }$ = $e ^ { x + 7 }$

Simplify -( $2 ^ { - x ^ { 2 } }$ $( x + 1 ) / x$ Enter your answer exactly in the form $2 \mathrm { P } ( \mathrm { x } )$ where P is a polynomial.

Use logarithmic differentiation to differentiate. - $3 ^ { x }$ Enter your answer as just $a b$ ln c.