_____2.
_____3.
GENERAL MATHEMATICS REVIEWER
Suppose that the amount of bacteria doubles every T units of time. If yo is the initial amount, then the
quantity after t units is given by ?
165𝑥 = 643𝑥+4 is an example of?
An exponential function with base b is a function of the form 𝑓(𝑥) = 𝑏 𝑥 or 𝑦 = 𝑏 𝑥 where b should be?
_____4.
Give an example of exponential equation.
_____5.
Suppose that the bacteria doubles every 50 hours. Give an exponential model for the bacteria as a
function of t. Let t = time in days. At 𝑡 = 0 there were initially 10 bacteria.
_____6.
Solve for the value of a: 𝟑𝒂+𝟓 = 𝟐𝟕𝟐𝒂 ?
_____7.
Given the exponential equation 325𝑥 = 644𝑥+4 . What should be the base for both sides of the
equation to solve the value of x?
_____8.
What property of exponent is used in finding the value of 643 =4?
_____1.
1
For items 9&10: Refer to the given exponential inequality below.
1 𝑥+5
1 (3𝑥)
( )
≥ (
)
10
100
_____9.
What values of x will satisfy the exponential inequality?
_____10.
Is there a need to reverse the direction of the inequality sign after finding the base for both sides?
_____11.
What are the 3 laws of logarithms?
_____12.
Properties of exponential function.
_____13.
Solve for x: 25𝑥 < 125𝑥−3
_____14.
Find the value of the unknown in 𝟒𝒙−𝟏 = 𝟏𝟔
For items 15-16, find the value of x in the given equations.
_____15.
log 3 (𝑥 + 4) = log 3 (2𝑥 − 4)
_____16.
log 2 (3𝑥 + 5) ≥ log 2 (𝑥 − 9)
_____17.
What are the basic properties of logarithms?
_____18.
What logarithmic expression expresses a relationship between two variables such as x and y?
_____19.
Calculate the approximate decibel level associated if a typical concert’s sound intensity is 10−7 𝑤/𝑚2 .
_____20.
Suppose that the decibel level of sound in a quiet office is 10−6 𝑤𝑎𝑡𝑡𝑠/𝑚2. What is the corresponding
sound intensity in decibels?
_____21.
Suppose that a 1-liter solution contains 10−4moles of hydrogen ions. What is its pH level?
_____22.
John and Peter are solving (0.6)𝑥−3 > (0.36)−𝑥−1 . Did anyone of them get the correct solution?
John
Peter
(0.6)𝑥−3 > (0.36)−𝑥−1
(0.6)𝑥−3 > (0.36)−𝑥−1
(0.6)𝑥−3 > (0.6)2(−𝑥−1)
(0.6)𝑥−3 > (0.6)2(−𝑥−1)
𝑥−3
−2𝑥−2
(0.6)
> (0.6)
(0.6)𝑥−3 > (0.6)−2𝑥−2
𝑥 − 3 > −2𝑥 − 2
𝑥 − 3 < −2𝑥 − 2
3𝑥 > 1
3𝑥 < 1
1
1
𝑥 >3
𝑥 <3
_____23.
Find the value of the given logarithmic expression using the three basic properties of logarithm,
𝑙𝑜𝑔5 125.
_____24.
What property of logarithms is used to find the value of 7log7 2 = 2?
_____25.
Using the laws and properties of logarithms, what is the correct expanded and simplified value of
𝑙𝑜𝑔2 81 ?
Principal
(P)
(26)
15,000
600
1,300
Rate
(r)
7%
(27)
4%
5%
Time
(t)
2 years
6 years
(28)
6 years
Interest
(I)
630.00
2,700
216.00
(29)
_____30.
For items 30 & 31:
Ms. Ehna invested Php 30,000 in a company that offers 5% interest compounded annually. How much
will this investment be worth at the end of each year for the next 3 years?
What is the exponential model for the given situation?
_____31.
How much will this investment be worth at the end of each year for the next 3 years?
_____32.
There are two things to remember when solving logarithmic inequalities. Which of the following of the
following does NOT belong?
A. The direction of the inequality
C. The direction of the inequality (< or >) is
(< or >) is based on whether the base b is based on whether the base b is greater than
equal to 1.
1 or less 1.
B. Check the resulting x value do not
D. None of these.
make any of the logarithms undefined.
_____33.
What is the formula for simple interest?
_____34.
Suppose that you invest P5,000 at 8% simple interest. How much money will you have after 6 years?
_____35.
_____36.
Find the compounded amount on P1,000 for 3 years at 7%.
Expand the expression in terms of the logarithms of the factors using the law of logarithms, log(𝑚𝑛3 ).
_____37
What are the basic properties of logarithms?