Pre-Calculus A
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3.2 Review Worksheet
In Exercises 1-4, write the logarithmic equation in exponential form.
3
1) log3 81 = 4
2) 𝑙𝑜𝑔16 8 =
3) ln 4 =1.3862
4)
4
1
ln 𝑒 2 = −2
In Exercises 5-8, write the exponential equation in logarithmic form.
5) 82 = 64
6) 93/2 = 27
7)
e2.5 = 12.1824…
8)
3
√𝑒 = 1.3956
In Exercises 9-12, evaluate the function at the indicated value of x without using a
calculator.
9) f(x) = log5 x when x = 25
11) f(x) = log10 x when x = 10,000
10) f(x) = log81 x when x = 9
12) f(x) = log10 x
when x =
1
1000
In Exercises 13-14, use a calculator to evaluate the function at the indicated value of x.
Round your result to three decimal places.
13)
f(x) = 3 log10 x when x = 15
14)
f(x) = ln x when x = 5
In Exercises 15-17, solve the equation for x.
15) log3 4x = log316
16) log4 43 = x
17) log8 x = log8 3-2
In Exercises 18-19, use the properties of logarithms to rewrite the expression.
1
18) log6 62x
19)
𝑙𝑜𝑔 16
4
4
In Exercises 20-21, use the properties of natural logarithms to rewrite the expression.
20) -ln e
21) 7 ln e0
In Exercises 22-23, find the domain, vertical asymptote, and x-intercept of the logarithmic
function, and sketch its graph by hand
22)
𝑦 = 1 + 𝑙𝑜𝑔2 (𝑥 − 2)
23)
𝑦 = 1 + 𝑙𝑛(𝑥 − 2)
24)
Home Mortgage The model 𝑡 = 16.625 ln (
𝑥
𝑥−750
) , x > 750
approximates the length of a home mortgage of $150,000 at 6% in terms of the monthly
payment. In the model, t is the length of the mortgage in years and x is the monthly
payment in dollars.
A) Use the model to approximate the lengths of a $150,000 mortgage at 6% when the
monthly payment is $897.72 and when the monthly payment is $1659.24
B) Approximate the total amounts paid over the term of the mortgage with a montly
payment of $897.72 and with a monthly payment of $1659.24. What amount of the total
is interest for each payment?