Algebra II : Simplifying Logarithms
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Example Questions
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 #51 : Simplifying 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 #52 : Simplifying 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 #53 : Simplifying Logarithms
True or false: 
False
True
True
By the Change of Base Property of Logarithms, if 
Substituting 7 for 
The correct choice is "true."
Example Question #1 : Logarithms With Exponents
In this question we will use the notation 
Find 
We can use the Property of Equality for Logarithmic Functions to take the logarithm of both sides:
Use the Power Property of Logarithms:
Divide each side by 
Use a calculator to get:
or
Example Question #1 : Logarithms With Exponents
Simplify
Using Rules of Logarithm recall:
Thus, in this situation we bring the 2 in front and we get our solution.
Example Question #51 : Simplifying Logarithms
Simplify the following equation.
We can simplify the natural log exponents by using the following rules for naturla log.
Using these rules, we can perform the following steps.
Knowing that the e cancels the exponential natural log, we can cancel the first e.
Distribute the square into the parentheses and calculate.
Remember that a negative exponent is equivalent to a quotient. Write it as a quotient and then you're finished.
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