𝒍𝒐𝒈 𝟒
𝒍𝒐𝒈 𝟏𝟐
Is the function f x = −3 4
or decay function?
𝑥−1
− 2 an exponential growth
𝒚 = 𝟐𝟓𝟎𝟎𝟎(𝟎. 𝟖𝟓)
Is the function f x =
decay function?
1 𝑥
( ) +1
2
an exponential growth or
𝒕
$1114.17
What is the domain and range of the function f x = 5𝑥+3 ?
𝟏𝟎
𝟕
Where is the asymptote of the function
y = 𝑙𝑜𝑔4 𝑥 − 1 − 2?
Growth
Simplify the expression
4(27𝑒 13 𝑥)
3𝑒 7 𝑥 −3
𝒍𝒐𝒈𝟑 𝟓𝟎
Rewrite the 𝑙𝑜𝑔7 343 = 3 as an exponential function.
Decay
Find the inverse of the function f x = 2𝑥 − 3.
Ln 6 + 2 ln x – 4 ln y
Find the inverse of the function f x = 6 log x.
X=9
You deposit $800 in an account that pays 4% annual
interest compounded continuously. What is the balance
after 5 years?
𝐥𝐨𝐠 𝟖
𝐥𝐨𝐠 𝟑
A new car costs $25,000. The value of the car decreases
by 15% each year. Write an exponential decay model
giving the car’s value y (in $) after t years.
𝒚 = 𝒍𝒐𝒈𝟐 (𝒙 + 𝟑)
You want to have $3000 in your savings account after 3
years. How much will you need to deposit of the account
pays 2.25% annual interest compounded quarterly?
𝟑
𝟕 = 𝟑𝟒𝟑
Expand 𝑙𝑜𝑔7 5𝑥 3 𝑦𝑧 2 .
3 2
6𝑒 𝑥
Expand
6𝑥 2
ln 4 .
𝑦
X = 0.327
Condense 5𝑙𝑜𝑔4 2 + 7𝑙𝑜𝑔4 𝑥 + 4𝑙𝑜𝑔4 𝑦.
X = -1
Condense 2 𝑙𝑜𝑔3 20 − 𝑙𝑜𝑔3 4 + 0.5𝑙𝑜𝑔3 4.
𝒙−𝟔
𝒚 = 𝟏𝟎
Rewrite the 𝑙𝑜𝑔3 8 by using the Change-of-Base formula.
D: (-∞, +∞)
R: (0, +∞)
Rewrite the 𝑙𝑜𝑔12 4 by using the Change-of-Base formula.
$2804.71
Solve log 7x + 4 = 5.
𝟕 𝟒
𝒍𝒐𝒈𝟒 𝟑𝟐𝒙 𝒚
Solve 𝑙𝑜𝑔6 3𝑥 + 𝑙𝑜𝑔6 𝑥 − 1 = 3.
𝒍𝒐𝒈𝟕 𝟓 + 𝟑𝒍𝒐𝒈𝟕 𝒙 + 𝒍𝒐𝒈𝟕 𝒚 + 𝟐𝒍𝒐𝒈𝟕 𝒛
Solve
3 3𝑥
𝑒
4
− 8 = −6.