Evaluating More Logs!
No calculator:
Evaluate log4(16).
2
f-1(x)=(1/2)x-1.
What is the pH of ice tea with a hydrogen ion concentration of 0.000158 moles per liter?
-log(0.000158) is approximately 3.8
Evaluate log(10x-3).
x-3
2x+1=23x
x=1/2
No calculator:
log9(3)
log3(3)/log3(9)=1/2
f(x)=(4/9)x-8. Find f-1(x).
f-1(x)=(9/4)x+18.
A quantity of insulin used to regulate sugar in the bloodstream breaks down by about 5% each minute. A body-weight adjusted dose is generally 10 units. Write a function representing the amount of that dose that remains after x minutes, and use it (by table or graph) to find out how long it takes for one-fourth of the dose to remain.
f(x)=10(0.95)x
Let Y1=10(0.95)x
and Y2=2.5
The two intersect by x=28,
So it will take 28 minutes for one-fourth of the dose to remain.
Evaluate ln(e45w)
45w
Solve, using a calculator (round to three decimal places):
2.43x+1=9
0.503
No calculator:
Evaluate log2(0.25).
=-2
Eliza's auto repair bill includes $175 for parts and $35 per hour for labor. The bill can be expressed as a function of hours x with the function f(x)=175+35x. Which statement explains the meaning of the inverse function?
A) Number of hours as a function of the total bill
B) Total bill as a function of the number of hours
C) Cost per hour as a function of the total bill
D) Total bill as a function of the cost per hour
A) because the roles of x and f(x) are swapped when we write the inverse.
Read this clue to yourself:
The number e, approximately equal to 2.71828, is named for the Swiss mathematician, Leonard Euler.
How is "Euler" pronounced?
Oiler
No calculator:
Evaluate log5(50)
0
Solve, no calculator:
log(50)+log(x/2)=2
x=4
Evaluate log5(52)+3log1/2(8).
log5(52)=2
log1/2(8)=-3
2+3(-3)=2-9=-7.
A clerk needs to price a digital camera returned by a customer. The customer paid a total of $103.14, which included a gift-wrapping charge of $3, and 8% sales tax. What was the original price? (Hint: Write the total cost c as function of the original price, p. Solve for p, then plug in 103.14 for c.)
$92.50
No calculator:
Solve 9-5x=(1/3)10
x=1
No calculator:
Simplify as much as possible.
log(103x+5)+10log(3x)
6x+5
Solve, calculator allowed:
2-log(3x)=log(x/12)
x=20
No calculator:
Evaluate log0.1(-90).
Undefined.
The formula C=(5/9)(F-32) gives degrees Celsius as a function of degrees Fahrenheit. Find the inverse of this function, and use it to find 16oC in degrees Fahrenheit.
60.8o
Solve (calculator permitted). Round your answer to four decimal places.
102x+1=90
0.4771
x=(log(90)-1)/2
No calculator:
Simplify as much as possible:
84x - log8(820-5x)
9x-20
Solve, no calculator:
62x-3=(1/36)-x-2
No solution.