Chapter 3 - Logarithms and Exponential Functions

Exponentially Fun

100

Using the one-to-one property, this is the answer to (1/3)^x-2=81. 

What is x=-2.

200

The value of a car 2 years after being purchased that originally cost 14,000 using the formula V(t)=14000(3/4)^t.

What is $7875.

300

The value of x for e^8-2x=e^-3. 

What is 11/2 or 5.5.

400

This amount is when a particular person turns 35 that has an account with an initial investment of 50,000 into a trust fund that has an interest rate of 8.75% that is compounded continuously. 

What is $1,069,047.14.

500

This is the amount that is given to a college after an initial deposit of $5000 within a trust fund that pays 7.5% interest, compounded continuously after 50 years. 

What is $212,605.41.

Logarithmic Amazement

100

This is what x is equal to within log₈(3x-2)=log₈5. 

What is 5. 

200

This is equal to the shoulder height of a male American elk with antler spread of 55 inches within h=116*log(a+40)-176 where a represents the antler spread and shoulder height h. 

What is 53.4 inches. 

300

Without the use of a calculator, this is the function value of f(x)=log₉x where x=3. 

What is 1/2. 

400

This value of x satisfies ln(x+9)=ln(4). 

What is -5. 

500

The number of miles, s, of roads cleared of snow is approximated by the model: s=25-((13*ln(h/12))/(ln3)) where h is the depth of the snow in inches. This value of s is when h=10 inches. 

What is 27.16 miles. 

Da Props of Logs

100

This is the value of log_1/25 rounded to three decimal places. 

What is -2.322. 

200

Rewriting and simplifying the logarithmic expression gives this answer to ln(3e^-4) rounded to three decimals.

What is -2.901. 

300

Using the properties of logarithms, this is the expansion of log₅5x². 

What is 1+2log₅x. 

400

Using the properties of logarithms, this is the expansion of ln((x+3)/xy). 

What is ln(x+3)-lnx-lny. 

500

When condensing this expression, log₆y-2*log₆z, we obtain this as a single logarithmic quantity. 

What is log₆(y/z²). 

Solving For Dat Unknown

100

This number satisfies log₄x=2. 

What is x=16. 

200

This result, rounded to three decimal places, solves the exponential equation 2^x+13=35. 

What is 4.459. 

300

Solving this exponential equation, 2(12^x)=190, to three decimals we obtain the correct x value. 

What is x=1.833. 

400

Solving the exponential equation for the unknown variable, -4(5^x)=-68, gives us this answer rounded to three decimal places. 

What is x=1.760. 

500

This number, rounded to three decimal places, solves for x within the equation 25e^-0.3x=12. 

What is x=2.447. 

Solving Madness

100

This value, rounded to three decimal places, solves the following equation: (1025/(8+e^4x))=5.

What is x=1.321. 

200

This value, rounded to three decimal places, solves the following equation: ln(x)=1/2. 

What is x=1.649. 

300

This value, rounded to three decimal places, solves the following equation: 18+4*ln(x)=7. 

What is x=0.0639. 

400

This value, rounded to three decimal places, solves the following equation: log(x)-log(8-5x)=2. 

What is x=1.597. 

500

This value, rounded to three decimal places, solves the following equation: 3e^-5x=132. 

What is x=-0.757.