Lesson 6.3 Logarithmic Functions (Page 370)
By: Cindy Chau 8-3
1. For any positive base b, where b ≠ 1: bx = y if and only if x = logby

Exponential
Logarithmic
102 = 100
2 = log10100
Exponent
Base

43 = 64  3 = log464
3 is the exponent and 4 is the base.

5 = log232  25=32
5 is the exponent and 2 is the base.

Memorize the formula and keep practicing problems to make it stick in your head.
2. Finding the approximate value

Log101026 = 3.01
You can solve the problem by using your calculator. Press LOG and put y, which
is1026, into the parentheses and then, press ENTER to get your answer.
3. Solving equations for x

10x = 12
x = log1012
Write the equation in logarithmic form (refer back to #1).
x = 1.08
Use your calculator (refer back to #2).
4. The logarithmic function y = logbx with base b, or x = by, is the inverse of the exponential
function y = bx, where b ≠ 1 and b > 0.
5. One-to-One Property of Exponents

If bx = by, then x = y.
6. Finding the value of v

v = log17289
17v = 289
Write the equation in exponential form (refer back to #1).
17v = 172
Use the One-to-One Property. (Refer back to #5)
v=2

3 = log6v
63 = v
Write the equation in exponential form (refer back to #1).
v = 216
Use your calculator.

Logv9 = 1/2
V1/2 = 9
Write the equation in exponential form (refer back to #1).
√V = 9
Fractional exponents can be written in a different form. √2 = 21/2
√V2 = 92
Square both sides to get rid of the square root sign.
v = 81
7. Calculating the [H+]

pH = 7
pH = -log10[H+]
7 = -log10[H+]
Substitute 7 for pH.
-7 = log10[H+]
Bring the negative to the other side by dividing by both sides by -1.
10-7 = [H+]
Write the equation into exponential form.
Practice Problems
1. Write each equation in logarithmic form.
a. 84 = 4096
b. 1251/3 = 5
c. (1/6)-2 = 36
2. Write each equation in exponential form.
a.
log327=3
b.
log41/16 = -2
3. Find the approximate value of each logarithmic expression.
a.
log108
b.
log1021,050
4. Solve each equation for x. Round your answers to the nearest tenth.
a.
10x = 3588
b.
10x = 3/49
5. Find the value of v in each equation.
a. v = log7343
b. -3 = log4v
c. logv216 = 3
6. Calculate [H+].
a.
pH = 10
b.
pH = 7.4
Answers
1. Write each equation in logarithmic form.
a. 4 = log84096
b. 1/3 = log1255
c. -2 = log1/636
2. Write each equation in exponential form.
a. 33=27
b. 4-2=16
3. Find the approximate value of each logarithmic expression.
a. .90
b. 4.32
4. Solve each equation for x. Round your answers to the nearest tenth.
a. x = 3.55
b. x = -1.21
5. Find the value of v in each equation.
a. v = 3
b. v = 1/64
c. v = 6
6. Calculate [H+].
a. [H+] = 10-10
b. [H+] = 10-7.4