Exponents
Exponentials pt. 2 (worth +100)
Logarithms
Logarithms pt. 2 (worth +100)
100

f(x) = 2x, what is f(4)?

f(4)=16

100

5x=14. 

Solve for x. Don't round until the final answer, and then round to 4 decimal places.

x=1.6397

100

log5 625= 4. Convert to the equivalent exponential form.

54=625

100

log7sqrt(7) = x. evaluate/solve for x without using a calculator.

( hint:how do we cancel out n2 using another exponent?)

x=1/2

200

graph 3^(x+5).

https://www.desmos.com/calculator/1uh0lxbaaz

200

e4x=6

0.448=x

200

2logx + 7logy. Condense the equation.

log(x2y7)

200

ln (1), find the value of the logarithm.

ln(1) = 0 

300

If f(x) = ax, and f(2)=25, find f(3).

f(3)=125

300

2-2x= 1/16

x=2

300

3logx + 8logy - log 3. Condense the Equation.

log ((x3y8)/3)

300

ln(3x+16)-lnx=ln4

x=16

400
e3.3673=29. Convert to a logarithmic statement.

ln29= 3.3673

400

2x+2=9x

0.922=x

400

log ((2x4y5)/z8). Expand the expression.

log 2 + 4logx + 5logy - 8logz

400

ln(3x+25)=ln(2x+14)

(hint: remember to check your work!)

no solution ("-11")

500

46x-3=256. Solve this exponential equation without logarithms.

x= 7/6 or 1.16

500

The amount of a certain radioactive material (in grams) in a storage facility at time t is given by 

C(t)=53e−0.11t  , where time is measured in years.

(a) How much of the radioactive material was present initially?

(b) What is the half-life of the radioactive material? (Hint: For what value of t is C(t)=26.5?) ( +100 Points)

a) 53 grams

b) 6.3 years.

500

log7730=x. Solve for x. Round to 6 decimal places.

(hint: lnx/lna)

x=3.388155

500

The average annual expenditures for a country's consumers of dairy products can be approximated by the function 

g(x)=35.8 + 141.6lnx, where x= 10 corresponds to 2010.

a) find 2014 and 2018.

b) (extra 100 points) assuming the model remains accurate, what is the first year where expenditures exceed $485?

a) g(14)=409.49, g(18)=445.08

b) x= 23.86, therefore the first year to exceed is x=24, or 2024.

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