Algebra II : Logarithms with Exponents
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Example Questions
Example Question #379 : Mathematical Relationships And Basic Graphs
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 #61 : Simplifying Logarithms
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 
The expression will simplify to:
The answer is:
Example Question #71 : Simplifying Logarithms
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 #72 : Simplifying Logarithms
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 #73 : Simplifying Logarithms
Which statement is true of 
By the Logarithm of a Power Property, for all real 
Setting 
Since, for any 
setting 
Example Question #74 : Simplifying Logarithms
Which statement is true of
for all integers 
Due to the following relationship:
can be rewritten as
By definition,
Set 
or, substituting back,
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