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Pearson Algebra 2 Common Core, 2011

PA

Pearson Algebra 2 Common Core, 2011 View details

End-of-Course Assessment

Exercise 69 Page 970

Use a calculator after applying the Change of Base Formula.

C

Practice makes perfect

We want to use the Change of Base Formula to evaluate the given expression.

lo g_{b} m = \frac{lo g _{c} m}{lo g _{c} b}

In the above formula,

m,

b,

and

c

are positive numbers, with

b \neq = 1

and

c \neq = 1 .

We will apply this formula to our expression.

lo g_{2} 3.2 = \frac{lo g 3 . 2}{lo g 2}

Recall that if the base of a logarithm is not stated, it is

10 .

For example,

lo g 3.2

=

lo g_{10} 3.2 .

Logarithms with this base are called common logarithms, and can be found using a calculator.

\frac{lo g 3 . 2}{lo g 2}

Calculate logarithm

\frac{0 . 5 0 5 1 4 9 \dots}{0 . 3 0 1 0 2 9 \dots}

Use a calculator

1.678071 \dots

Round to $1$ decimal place(s)

1.7

This corresponds to option C.

Subchapter links

Exercises p.964-971