solving logarithmic equations objective: solve equations with a “log” in them using properties...
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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?
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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).
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log3(3x) = _______
log4(42x) = _______
5log5
(x) = ________
3log3
(2x) = _______
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To solve a logarithmic equation make each side into an EXPONENTIAL equation with the same BASE
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Ex 1) Solve
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Ex 2) log4(5x + 1) = 2
5x + 1 = 42
5x + 1 = 16
5x = 15
x = 3
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You try!
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The common log will not show its base, remember that it is always ____________.
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Ex 3) Solve
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Ex 4)
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You Try!
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The natural log will not show its base, remember that it is always _______.
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Ex 5) Solve
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Ex 6)
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You Try!
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One log each side
then…
x = y
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Power Rule
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Product Property
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Quotient Property
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Use properties to re-write
a.
b.
c.
d.
)(log4 5 x
)5(log)(log 22 x
)5(log)(log 22 x
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Ex 7) One log each side
log5 (-3m – 1) = log5 (-4m – 6)
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Ex 8) Power Property
2log(x) = 5
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Ex 9) Product Property
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Ex 10) Quotient Property
2)4ln()ln( x
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Ex 11) Multiple Properties
4 log2 (x) + log2 (5) = log2 (405)
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Ex 12) Multiple Properties
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1. )16(log)4(log)(log3 555 x
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2. )32(log)13(log 44 xx
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3. 4)(log 35 x
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4.