Exponential and Logarithmic Jeopardy Review!!!

Exponential Functions

100

Rewrite in exponential form:

Log ₃(2x) = 7

3⁷ = 2x

200

What is the equation of the asymptote for 

f(x) = 3^x-4 + 2

y = 2

300

What is the domain and range for

 g(x) = (1/2)^x+1 + 3 

domain: (-inf, inf)

Range: (3, inf)

400

Find the ending amount of an investment of $10000 invested at 4% interest compounded monthly for 5 years.  

$12,209.97

500

Find the ending investment amount of $32,000 invested at 7% interest compounded continuously for 9 years.  

$60083.54

Logarithmic Functions

100

Convert to Logarithmic form:

Ln (x - 5) = (y + 2)

e^(y+2) = (x - 5)

200

What is the domain

  f(x) = log₂(x)

domain: (0, inf)

range: (-inf, inf)

300

Simplify:    log₅(1/125)

-3

400

Condense

5 lnx - 4 lny + 2 lnz

ln(x⁵z²/y⁴)

500

Expand

log[(2x+1)³/(5y-2)^1/2]

3log(2x+1) - (1/2)log(5y-2)

Exponential Equations

100

solve:

          3^{x + 4} =  81

x = 0

200

Determine the exact value of x:

     4e^2x+1 = 12

x = [-1 + ln(3)]/2

300

Determine the solution(s):

   e^2x - 4 = 0

x = ln(4)/2

400

Solve for x:

4^x-2 =  16^{2x + 1}

x = -4/3

500

solve for t: (round to the nearest whole number)

25000 = 5000(1 + .03/4)^4t

t = 54 years

Logarithmic Equations

100

Solve 

  log(3x + 3) = log(5x + 1) 

x = 1

200

 Solve 

   log₂(x - 3) = 5

x = 35

300

Solve:

  log₃(x) + log₃(x - 2) = 1

x = 3

400

Solve 

     log(4x - 2) -  log(2x + 1) = log(5)

No Solution

500

solve:

     (lnx)² = lnx

x = e, x = 1

Misc.

100

Exponential and Logarithmic Functions are _______

functions of each other as long as ____________. 

inverse

bases are the same

400

What is the property that allows you to solve equations with logarithms on both sides?

If Log_aX = Log_aY then X = Y

500

Simplify  (no Calculator)

Ln(e⁴) + Log₂(1/64) - Log (0.00001)

3