Logarithms with Other Bases (6.9)

Solving the three parts of logarithmic equations

Review with a POD

What we’ve seen so far: If y = bx, then x = logby.

Vocabulary review:x is the b is they is the

There are certain conditions b and y must meet:y > 0b > 0 and b cannot equal 1 (why

not?)

Review with a POD

What we’ve seen so far: If y = bx, then x = logby.

When we write with logs we’re solving for the exponent:

The exponent is by itself.b is the base (in the basement).

Rewrite to solve for t: m = 8.5t.

Review with a POD

What we’ve seen so far: If y = bx, then x = logby.

Rewrite these statements using logs:

10x = 5.

6x = 4/3

2x = 8

How would you solve any of them?

Solving for the exponent

1. log2 8 = x

2. log3 81 = x

3. log4 32 = x

Solving for the exponent

1. log2 8 = x 2x = 8 x = 3 using guess and

check or common baseYou could also set it up with the change of base.

2. log3 81 = x 3x = 81 x = 4 ditto

3. log4 32 = x4x = 32 x = 2.5 ditto

Solving for the argument

What is the argument again?

1. log3 x = -4

2. log5 x = 5

3. log4 x = 0

How could you check your answers?

Solving for the argument

1. log3 x = -4

3-4 = x x = 1/81

2. log5 x = 555 = x x = 3125

3. log4 x = 0

40 = x x = 1

Solving for the base

What is the base again?

1. logx 8 = 3

2. logx 25 = 2/3

How could you check these answers?

Solving for the base

1. logx 8 = 3x 3 = 8(x3)1/3 = 81/3

x = 2

2. logx 25 = 2/3x 2/3 = 25(x2/3)3/2 = 253/2

x = 125