Exponential & Logarithmic Expressions
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The exponential expression:
base
These expressions are inverses of one another.
b
Exponential & Logarithmic Expressions
x
power
=
y
number
power
Can be rewritten to solve
for the power as:
x
=
log  y
base
b
number
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Examples:
Exponential & Logarithmic Expressions
Logarithm     to     Exponential form.
When we take base "8" tothe power of "2" we get 64.
When we take base "144" tothe power of "½" we get 12.
When we take base"11" to the power of"-2" we get 1/121.
Think
1441/2 = 12
11-2
82 = 64
Write
  1
121
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Exponential & Logarithmic Expressions
Logarithm     to     Exponential form.
Answer:
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Exponential & Logarithmic Expressions
Logarithm     to     Exponential form.
Answer:
=
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Exponential & Logarithmic Expressions
Logarithm     to     Exponential form.
Answer:
=
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Exponential & Logarithmic Expressions
Logarithm     to     Exponential form.
Answer:
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Exponential & Logarithmic Expressions
Logarithm     to     Exponential form.
Answer:
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Exponential & Logarithmic Expressions
Logarithm     to     Exponential form.
Answer:
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Exponential & Logarithmic Expressions
Logarithm     to     Exponential form.
Answer:
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Examples:
Exponential & Logarithmic Expressions
Exponential     to     Logarithm form.
The log base "3" of "9" is "2".
The log base "7" of "1/49" is "-2".
The log base "625" of "5" is "¼".
Think
log7(    )=-2
log6255=
log39=2
 1
49
Write
1
4
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Exponential & Logarithmic Expressions
Exponential     to     Logarithm form.
Answer:
=log
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Exponential & Logarithmic Expressions
Exponential     to     Logarithm form.
Answer:
=log
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Exponential & Logarithmic Expressions
Exponential     to     Logarithm form.
Answer:
=log
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Exponential & Logarithmic Expressions
Exponential     to     Logarithm form.
Answer:
=log
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Exponential & Logarithmic Expressions
Exponential     to     Logarithm form.
Answer:
=log
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Exponential & Logarithmic Expressions
Exponential     to     Logarithm form.
Answer:
=log
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Exponential & Logarithmic Expressions
Exponential     to     Logarithm form.
Answer:
=log
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Exponential & Logarithmic Expressions
Exponential     to     Logarithm form.
Answer:
=log
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Exponential & Logarithmic Expressions
Exponential     to     Logarithm form.
Answer:
=log
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Examples:
When logarithmic expressions contain numbers that are easy powers
of the base, exact values can be determined with out a calculator.
Exponential & Logarithmic Expressions
What power do you have to raise base "4" to in order to get "1/64" as an answer?I need a negative power to get a fractionand I know that 43 is 64.
What power do you have to raise base "2" to in order to get "8" as an answer?I know that 23 is 8.
Think
So . . .  log4(    ) = -3
So . . .  log28 = 3
Write
 1
64
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Exponential & Logarithmic Expressions
Exact Values of Logarithmic Expressions
Answer:
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Exponential & Logarithmic Expressions
Exact Values of Logarithmic Expressions
Answer:
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Exponential & Logarithmic Expressions
Exact Values of Logarithmic Expressions
Answer:
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Exponential & Logarithmic Expressions
Exact Values of Logarithmic Expressions
Answer:
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Exponential & Logarithmic Expressions
Exact Values of Logarithmic Expressions
Answer:
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Exponential & Logarithmic Expressions
Exact Values of Logarithmic Expressions
Answer:
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Exponential & Logarithmic Expressions
Exact Values of Logarithmic Expressions
Answer:
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Exponential & Logarithmic Expressions
Exact Values of Logarithmic Expressions
Answer:
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Exponential & Logarithmic Expressions
Exact Values of Logarithmic Expressions
Answer:
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Exponential & Logarithmic Expressions
Exact Values of Logarithmic Expressions
Answer:
log1010 = 1
Examples:
Your calculator can process logs of base 10. Use it now to calculate
the answer.
If 30 is between 10 and 100 . . . . 
What two values is log1030 between?
Sometimes logarithmic expressions contain numbers that are noteasy powers of the base. When that happens, a calculator is needed.
Answer: Round to 3 decimal places. ie. 2.567
Exponential & Logarithmic Expressions
log1030 =
?
log10100 = 2
< log1030 <
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Sometimes logarithmic expressions contain numbers that are noteasy powers of the base. When that happens, a calculator is needed.
Exponential & Logarithmic Expressions
=
=
=
=
=
Answer: Round to 3 decimal places.
            ie. 2.567
*If the answer is less than 1
put a leading zero before
your answer.

i.e. answer 0.123 not .123
Sometimes logarithmic expressions contain numbers that are noteasy powers of the base. When that happens, a calculator is needed.
log150
log467
log2000
log782
log1200
Exponential & Logarithmic Expressions
=
=
=
=
=
Answer: Round to 3 decimal places.
            ie. 2.567
*If the answer is less than 1
put a leading zero before
your answer.

i.e. answer 0.123 not .123
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