SOLVING LOGARITHMIC EQUATIONS Objective: solve equations with a “log” in them using properties...

SOLVING LOGARITHMIC EQUATIONS

Objective: solve equations with a “log” in them using properties of logarithms

How are log properties use to solve for unknown values?

Solving Logarithmic Equations

Remember that an exponential and a logarithm are INVERSES of each other.

Which means that they UN-DO each other (cancel out).

log3(3x) = _______

log4(42x) = _______

5log5

(x) = ________

3log3

(2x) = _______

To solve a logarithmic equation make each side into an EXPONENTIAL equation with the same BASE

Ex 1) Solve

Ex 2) log4(5x + 1) = 2

5x + 1 = 42

5x + 1 = 16

5x = 15

x = 3

You try!

The common log will not show its base, remember that it is always ____________.

Ex 3) Solve

Ex 4)

You Try!

The natural log will not show its base, remember that it is always _______.

Ex 5) Solve

Ex 6)

You Try!

One log each side

then…

x = y

Power Rule

Product Property

Quotient Property

Use properties to re-write

a.

b.

c.

d.

)(log4 5 x

)5(log)(log 22 x

)5(log)(log 22 x

Ex 7) One log each side

log5 (-3m – 1) = log5 (-4m – 6)

Ex 8) Power Property

2log(x) = 5

Ex 9) Product Property

Ex 10) Quotient Property

2)4ln()ln( x

Ex 11) Multiple Properties

4 log2 (x) + log2 (5) = log2 (405)

Ex 12) Multiple Properties

1. )16(log)4(log)(log3 555 x

2. )32(log)13(log 44 xx

3. 4)(log 35 x

4.