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MidChapter Log Test

Graphing

Identify the transformations applied to g(x)

Reflected: _____________

Shifted: _____________

3)2()( xxg

over x axis

up 3 units

Graphing

Identify the important places on g(x)

Horizontal Asymptote: __________

Y Intercept: __________

3)2()( xxg

y = 3

(0,2)

3)2()( xxg

Graphing The basic graph of

f(x) = (2)x is given.

Use this graph, along with your previous

answers to help sketch the graph of g(x).

y = 3

(0,2)

Solving Solve by using “matching bases.”

x = 3/2

123 55 xx

Solving Solve by using “matching bases.”

x = 1

xx 82 12

Form Write this exponential statement

as a logarithmic statement

log381=4

8134

Form Write this logarithmic statement

as a exponential statement

4-3 = 1/64

3log641

4

“think exponents” Evaluate each logarithm by

“thinking exponents.”

2

36log6

“think exponents” Evaluate each logarithm by

“thinking exponents.”

12

3

2 16log

Change of Base Formula

Use your calculator and the change of

base formula to find the missing exponent

5.19

3003 x

Condense Use properties of logarithms to condense

into a single logarithm

𝑙𝑜𝑔8

𝑥𝑦

yx loglog2log3

Expand Use properties of logarithms to expand

into three logarithms

𝑙𝑜𝑔43 + 2𝑙𝑜𝑔4𝑥 + 𝑙𝑜𝑔4𝑦

yx2

4 3log

Evaluate Use a combination of “wits” and properties

to evaluate.

X = 6

2

4 64log

Evaluate Use a combination of “wits” and properties

to evaluate.

X = 2

2log225log

Evaluate Use a combination of “wits” and properties

to evaluate.

X = 1

16log64log 44

Application If $50,000 gains 6% each year for 10 years.

Find the final value.

𝑦 = 50000(1 + .06)10

𝑦 = 50000(1.06)10

y = $89,542

xbay