Algebra II : Adding and Subtracting Logarithms
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Example Questions
Example Question #41 : Adding And Subtracting Logarithms
Combine the logs as one:
Evaluate each term. Write the property of logs when they are subtracted.
The remaining term is:
The answer is:
Example Question #41 : Adding And Subtracting Logarithms
Solve 
When you add logarithms of the same base, you multiply the terms inside the log:
A logarithm with a base that's the same as the term inside it is always equal to 
Example Question #42 : Adding And Subtracting Logarithms
Solve 
When adding logs with the same base, we multiply the terms inside of them:
Now we can expand the log again so that the terms inside of it match the base:
Example Question #51 : Simplifying Logarithms
Combine as one log:
According to log rules, whenever we are adding the terms of the logs, we can simply combine the terms as one log by multiplication.
The answer is:
Example Question #42 : Adding And Subtracting Logarithms
Simplify 
First we can make the coefficient from the left term into an exponent:
Next, remember that if we're subtracting logs, we divide the terms inside them:
Example Question #43 : Adding And Subtracting Logarithms
Simplify
When we add logs, we multiply the terms in them:
From here, we multiply them out:
Example Question #54 : Simplifying Logarithms
True or false: for all positive values of 
True
False
True
By the Product of Logarithms Property,
Setting 
"log" refers to the common, or base ten, logarithm, so, by definition,
if and only if
Setting
so
and 
The statement is true.
Example Question #55 : Simplifying Logarithms
True or false: 
False
True
False
A statement can be proved to not be true in general if one counterexample can be found. One such counterexample assumes that 
becomes
or, equivalently,
The word "log" indicates a common, or base ten, logarithm, as opposed to a natural, or base 
or
This is false, so 
Example Question #44 : Adding And Subtracting Logarithms
True or false:
for all negative values of 
False
True
False
It is true that by the Product of Logarithms Property,
However, this only holds true if both 
Example Question #45 : Adding And Subtracting Logarithms
True or false: 
True
False
True
By the Change of Base Property of Logarithms, if 
Substituting 7 for 
The correct choice is "true."
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