Lesson 4a – Introduction to Logarithms
MAT12x
Name ___________ Date __________
HW Packet
Lesson 4a – Introduction to Logarithms
Problem 1 Locate the LOG and LN button on your calculator. Use them to fill in the
missing values in the input/output table. When you use your calculator,
remember to close parentheses after your input value.
x
Function
5
Log(x)
5
Ln(x)
5
4Log(x)
5
Log(x)4
5
4+2Ln(x)
5
Log(x)/Log(2)
y
(x,y)
Problem 2 Rewrite each Logarithm as an exponential and then use the table function on
your calculator to find the answer. The first one is done for you.
Log
a)
Draw Log with
Loop
Exponential
5x = 125
Answer
Enter Y1 = 5^x into
the calculator
Look at your table and
find x when Y1 = 125
Answer: x = 3
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Lesson 4a – Introduction to Logarithms
MAT12x
b)
c)
d)
e)
f) log6 0 = x
Problem 3 Rewrite each exponent as a log. Then use the change of base rule and
your calculator to find the answer.
Exponential
x
a) 5 = 125
Draw Exp.
with Loop
x
5 = 125
Exponential
Change of Base
Answer
Enter into
calculator:
log(125)/log(5)
Answer: 3
b) 3x = 100
c) 4x = .5
d) 10x = 4025
e) ( )
f) 20x = 0
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Lesson 4a – Introduction to Logarithms
MAT12x
Problem 4 Solve each Logarithmic Function for X. Check your answer. First one
is done for you.
Logarithmic Equation
a) 4 + 2log4(x+3) = 8
4 + 2log4(x+3) = 8
-4
-4
2log4(x+3) = 4
2
2
Log4(x+3) = 2
Rewrite as an Exponent
42 = x+3
16 = x+3
-3
-3
13 = x
Final Answer x = 13
b) log5x = 4
c) log6x = -3
d) 2log7x = 8
e) 4+2log7x = 2
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Lesson 4a – Introduction to Logarithms
MAT12x
f) 8-2log7x = 10
g) log3x4 = 16
h) 8log3x2 = 48
i) 2 – 3log2x4 = 50
Problem 5 Google Time: The Earthquake of September 7, 1999 in Athens, Greece
measured 5.9 on the Richter Scale.
Find two earthquakes that were smaller and two that were larger. Determine
exactly how much smaller or larger the earthquakes were.
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