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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.
