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Example Questions
Example Question #1 : Properties Of Logarithms
Find the inverse function of the following exponential function:
Since we are looking for an inverse function, we start by swapping the x and y variables in our original equation.
Now we have to solve for y. To do this we have to work towards isolating y. First we remove the constant multiplier:
Next we eliminate the base on the right side by taking the natural log of both sides.
Subtract 1 and divide by 4:
Example Question #11 : Properties Of Logarithms
Condense the following expression into one logarithm:
To condense this, the second term must have the 2 in front moved inside.
When adding two logs, multiply their insides; when subtracting two logs, divide their insides.
Example Question #21 : Exponential And Logarithmic Functions
Expand the following log completely
To expand a logarithm, quantities in the inside that are multiplied get added and quantities in the inside that are divided get subtracted.
Example Question #22 : Exponential And Logarithmic Functions
Solve for :
The first step to solving this problem is to realize that
Then, the equation falls into the follow form which resembles a quadratic.
Let . Then,
Thus, and
.
Since ,
Example Question #23 : Exponential And Logarithmic Functions
Simplify the expression.
None of the above answers
Using the quotient rule for logarithms we can condense these two logarithms into a single logarithm.
We then obtain our answer by simple division.
Example Question #24 : Exponential And Logarithmic Functions
Simplify the expression.
Using the properties of logarithms we first simplify the expression to . Then we use the quotient rule for logarithms and cancel some terms to obtain our answer.
Example Question #25 : Exponential And Logarithmic Functions
Simplify the expression.
None of the other answers
Using the properties of logarithms we first rewrite the expression as . Now we combine the three pieces into the form
. We then obtain our answer when we combine the terms with
and cancel those with
.
Example Question #26 : Exponential And Logarithmic Functions
Solve for x:
Example Question #24 : Exponential And Logarithmic Functions
Which of the following is equivalent to ?
When multiplying exponents with a common base, you add both the exponents together. Hence,
When an exponent is raised to an exponent you multiply the exponents together. Hence, for you would multiply
to get
.
Answer:
Example Question #27 : Exponential And Logarithmic Functions
Solve the following for x:
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