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Example Questions
Example Question #11 : Logarithms With Exponents
Use
and
Evaluate:
Since the question gives,
and
To evaluate
manipulate the expression to use what is given.
Example Question #380 : Mathematical Relationships And Basic Graphs
Simplify:
According to log rules, when an exponential is raised to the power of a logarithm, the exponential and log will cancel out, leaving only the power.
Simplify the given expression.
Distribute the integer to both terms of the binomial.
The answer is:
Example Question #11 : Logarithms With Exponents
Simplify:
The natural log has a default base of
.This means that the expression written can also be:
Recall the log property that:
This would eliminate both the natural log and the base, leaving only the exponent.
The natural log and the base
will be eliminated.The expression will simplify to:
The answer is:
Example Question #11 : Logarithms With Exponents
Simplify:
The log property need to solve this problem is:
The base and the log of the base are similar. They will both cancel and leave just the quantity of log based two.
The answer is:
Example Question #14 : Logarithms With Exponents
Solve:
Rewrite the log so that the terms are in a fraction.
Both terms can now be rewritten in base two.
The exponents can be moved to the front as coefficients.
The answer is:
Example Question #381 : Mathematical Relationships And Basic Graphs
Which statement is true of
for all positive values of ?
By the Logarithm of a Power Property, for all real
, all ,
Setting
, the above becomes
Since, for any
for which the expressions are defined,,
setting
, th equation becomes.
Example Question #71 : Simplifying Logarithms
Which statement is true of
for all integers
?
Due to the following relationship:
; therefore, the expression
can be rewritten as
By definition,
.
Set
and , and the equation above can be rewritten as,
or, substituting back,
Example Question #1 : Solving Logarithms
Solve for
:
To solve for
, first convert both sides to the same base:
Now, with the same base, the exponents can be set equal to each other:
Solving for
gives:
Example Question #3041 : Algebra Ii
Solve the equation:
Example Question #3 : Solving Logarithms
Use
to approximate the value of .
Rewrite
as a product that includes the number :
Then we can split up the logarithm using the Product Property of Logarithms:
Thus,
.
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