EXPONENTIAL AND LOGARITHMIC PROPERTIES AND FUNCTIONS
THE LOGARITHMIC FUNCTION
USING LOGARITHMS TO SOLVE EXPONENTIAL EQUATIONS
SCIENTIFIC NOTATION
APPLICATIONS OF EXPONENTS AND LOGARITHMS
100
e2*e-4*e9
e7
100
Graph and state the domain and range.
𝑓(𝑥) = log2 𝑥
𝐷: 𝑥 > 0
𝑅: 𝑦 ∈ ℝ
100
3(5^(2t-4))=75
3
100
Rewrite the number in standard form:
8.1065 x 107
81,065,000
100
How many years will it take an account to triple in value, assuming a 9.1% interest rate compounded monthly?
12.12 years
200
(k^2m^3)/(14e^4)div(m^4n^2)/(7e^7)
(k^2e^3)/(2m^2n^2)
200
Graph and state the domain and range.
ℎ(𝑥) = − log2(𝑥 − 1)
𝐷: 𝑥 > 1
𝑅: 𝑦 ∈ ℝ
200
42r+3=1
-3/2 or -1.5
200
Rewrite the number in standard form:
987.045 x 10-4
0.0987045
200
If interest is compounded twice a year, at what annual rate must you invest $2000 to have $3000 at the end of 6 years?
6.8732%
300
Graph and state the domain and range. Describe the transformation from the parent function.
h(x)=2^-x+1
𝐷: 𝑥 ∈ ℝ (all real numbers)
𝑅: 𝑦 > 1
Reflected over the y-axis and shifted up 1.
300
Graph and state the domain and range
𝑛(𝑥) = ln 𝑥 + 3
𝐷: 𝑥 > 0
𝑅: 𝑦 ∈ ℝ
300
5^(8x+17)=1/125
-20/8 or -5/2
300
Evaluate the expression. Write your answer in scientific notation.
(6 x 1020)(3 x 10-20)
1.8 x 101
300
If a 1000-gram sample of radioactive material loses 2% of its mass every year, how much will there be after 60 years?
297.553
400
Graph and state the domain and range. Describe the transformation from the parent function.
n(x)=ex-2
𝐷: 𝑥 ∈ ℝ (all real numbers)
𝑅: 𝑦 > 0
Shift right 3.
400
Graph and state the domain and range.
𝑞(𝑥) = − log(𝑥 − 6) + 1
𝐷: 𝑥 > 6
𝑅: 𝑦 ∈ ℝ
400
3^(m-6)+4=13
8
400
Evaluate the expression. Write your answer in scientific notation.
(5.034*10^20+2.9*10^19)/(4.0*10^22)
1.331 x 10-2
400
Assume a radioactive material decays continuously at a rate of 𝑘. If 2000 grams decayed to 1200 grams in one year, what is the value of 𝑘?
40%
500
Graph and state the domain and range.
z(x)=-e2x+4
𝐷: 𝑥 ∈ ℝ (all real numbers)
𝑅: 𝑦 < 4
500
Graph and state the domain and range
z(x)=1/2logx
𝐷: 𝑥 > 0
𝑅: 𝑦 ∈ ℝ
500
e^(4x-1)+3=20
(ln17+1)/4 or 0.958
500
Evaluate the expression. Write your answer in scientific notation.
1.00251div(3*10^-3)
3.3417 x 102
500
A basic substance has a pH value of 11.5. What is its hydrogen ion concentration in moles per liter?
3.16 x 10-12