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Example Questions
Example Question #1 :Exponential Functions
Solve:
The answer does not exist.
To solve, it is necessary to know the property of.
Sinceand theterms cancel due to inverse operations, the answer is what's left of theterm.
The answer is:
Example Question #1 :对数和指数
Which equation is equivalent to:
,
So,
Example Question #1 :Exponential And Logarithmic Functions
What is the inverse of the log function?
This is a general formula that you should memorize. The inverse ofis. You can use this formula to change an equation from a log function to an exponential function.
Example Question #1 :Exponential Functions
Rewrite the following expression as an exponential expression:
Rewrite the following expression as an exponential expression:
记得以下日志和指数的性质s:
Can be rewritten in the following form:
So, taking the log we are given;
We can rewrite it in the form:
So b must be a really huge number!
Example Question #2 :Exponential And Logarithmic Functions
Convert the following logarithmic equation to an exponential equation:
Convert the following logarithmic equation to an exponential equation:
Recall the following:
This
Can be rewritten as
So, our given logarithm
Can be rewritten as
Fortunately we don't need to expand, because this woud be a very large number!
Example Question #1 :College Algebra
Convert the following logarithmic equation to an exponential equation.
Convert the following logarithmic equation to an exponential equation.
To convert from logarithms to exponents, recall the following property:
Can be rewritten as:
So, starting with
,
We can get
Example Question #7 :Exponential Functions
Solve the following:
To solve the following, you must "undo" the 5 with taking log based 5 of both sides. Thus,
The right hand side can be simplified further, as 125 is a power of 5. Thus,
Example Question #1 :Exponential And Logarithmic Functions
Solve for:
(Nearest hundredth)
The equation has no solution.
Apply the Product of Powers Property to rewrite the second expression:
Distribute out:
Divide both sides by 5:
Take the natural logarithm of both sides (and note that you can use common logarithms as well):
Apply a property of logarithms:
Divide byand evaluate:
Example Question #2 :Exponential Functions
Solve for:
(Nearest hundredth, if applicable).
The equation has no solution.
, so rewrite the expression at right as a power of 3 using the Power of a Power Property:
Set the exponents equal to each other and solve the resulting linear equation:
Distribute:
Subtractand 1 from both sides; we can do this simultaneously:
Divide by:
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