Algebra II : Mathematical Relationships and Basic Graphs
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Example Questions
Example Question #5 : Solving Logarithms
Solve for 
To solve this logarithm, we need to know how to read a logarithm. A logarithm is the inverse of an exponential function. If a exponential equation is
then its inverse function, or logarithm, is
Therefore, for this problem, in order to solve for 
which is 
Example Question #7 : Solving Logarithms
Solve for 
Logs are exponential functions using base 10 and a property is that you can combine added logs by multiplying.
You cannot take the log of a negative number. x=-25 is extraneous.
Example Question #1 : Solving Logarithms
If 
This question is testing the definition of logs. 
In this case, 
Taking square roots of both sides, you get 
Example Question #9 : Solving Logarithms
Rewriting Logarithms in Exponential Form
Solve for 
Which of the below represents this function in log form?
The first step is to rewrite this equation in log form.
When rewriting an exponential function as a log we must remember that the form of an exponential is:
When this is rewritten in log form it is:
Therefore we have 
Example Question #10 : Solving Logarithms
Solve for 
Not enough information
Use the rule of Exponents of Logarithms to turn all the multipliers into exponents:
Simplify by applying the exponents: 
According to the law for adding logarithms, 
Therefore, multiply the 4 and 7.
Because both sides have the same base, 
Example Question #391 : Mathematical Relationships And Basic Graphs
Evaluate 
No solution
In logarithmic expressions, 
Therefore, the equation can be rewritten as 
Both 8 and 128 are powers of 2, so the equation can then be rewritten as 
Since both sides have the same base, set 
Solve by dividing both sides of the equation by 3: 
Example Question #151 : Logarithms
Solve the equation for 
No solution
Because both sides have the same logarithmic base, both terms can be set equal to each other:
Now, evaluate the equation.
First, add x to both sides:
Add 15 to both sides:
Finally, divide by 6: 
Example Question #51 : Exponential And Logarithmic Functions
Solve this logarithmic equation:
None of the other answers.
To solve this problem you must be familiar with the one-to-one logarithmic property.
one-to-one property:
isolate x's to one side:
move constant:
Example Question #52 : Exponential And Logarithmic Functions
Solve the equation:
No solution exists
Get all the terms with e on one side of the equation and constants on the other.
Apply the logarithmic function to both sides of the equation.
Example Question #53 : Exponential And Logarithmic Functions
Solve the equation:
Recall the rules of logs to solve this problem.
First, when there is a coefficient in front of log, this is the same as log with the inside term raised to the outside coefficient.
Also, when logs of the same base are added together, that is the same as the two inside terms multiplied together.
In mathematical terms:
Thus our equation becomes,
To simplify further use the rule,
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