Chapter Eighteen — Logarithmic Functions

The Humongous Book of Algebra Problems

400

Evaluating Logarithmic Expressions

Given log

a

b = c, nd a, b, or c

18.1 Express the logarithmic equation log

a

b = c as an exponential equation.

The logarithmic equation log

a

b = c is equivalent to the exponential equation

a

c

= b.

18.2 Identify the value of n that completes the equation: log

2

n = 3.

According to Problem 18.1, log

2

n = 3 is equivalent to the exponential equation

2

3

= n.

18.3 Identify the value of n that completes the equation: log

6

n = –2.

Rewrite the logarithmic equation as an exponential equation.

6

–2

= n

Eliminate the negative exponent and simplify.

18.4 Identify the value of n that completes the equation: .

Rewrite the logarithmic equation as an exponential equation.

27

1/3

= n

Rewrite 27

1/3

as a radical expression and simplify.

This

expression is read

“log base a of b

equals c.”

A negative

power means “the

reciprocal of.” The

reciprocal

of 6

2

is .

If you

need to review

how fractional

exponents work, ip

back to Problems

13.13–13.17.

The cube

root of 27 is 3

because 3 cubed

equals 27.

Chapter Eighteen — Logarithmic Functions

The Humongous Book of Algebra Problems

401

18.5 Identify the value of n that completes the equation: log

4

16 = n.

Rewrite the logarithmic equation as an exponential equation.

4

n

= 16

Write both sides of the equation as powers of 4.

18.6 Identify the value of n that completes the equation: log

25

5 = n.

Rewrite the logarithmic equation as an exponential equation.

25

n

= 5

Write both sides of the equation as powers of 5 and solve for n.

18.7 Identify the value of n that completes the equation: log

10

10 = n.

Rewrite the logarithmic equation as an exponential equation.

10

n

= 10

Write both sides of the equation as powers of 10 and solve for n.

18.8 Identify the value of n that completes the equation: log

n

1,000 = 3.

Rewrite the logarithmic equation as an exponential equation.

n

3

= 1,000

Solve for n by taking the cube root of both sides of the equation.

If two

equal bases

are raised

to exponents

and the results

are equal, the

exponents must be

equal as well. In

other words, you

can drop the

bases and set

the powers

equal.

5

2

is raised

to the n power.

When something to

a power is raised to

a power, multiply the

exponents:

(5

2

)

n

= 5

2

˙

n

= 5

2n

.

The expression

log

c

c always equals

1; c can be any

pos-itive number

except 1.

Start Free Trial

No credit card required