SOLUTION: Solve for the approximate value of x: In x=3 Is it 3?

Question 86948: Solve for the approximate value of x: In x=3
Is it 3?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
By "In" I believe you mean "ln" which is the notation for natural logarithms. Natural
logarithms have the base e which is the symbol for a number that is approximately 2.718281828 ...
.
This is a problem in which you can use a translation from logarithmic form to the equivalent
exponential form. This translation is done according to the following rule:
.
is equivalent to the exponential form
.
In your problem, the "ln" tells you that you are using a logarithm with the base e. Therefore,
your problem can be written:
.

.
and by comparing this to the translation rule you can tell that b = e, C = 3, and A = x.
Substitute these values into the exponential form and you get an exponential form of:
.

.
So you now know that and since e is approximately 2.718281828 you can get
an approximate value for x by using the equation:
.

.
You can then use a calculator to cube 2.718281828 and you will get:
.

.
as a pretty close approximation of the value of x.
.
Remember that translation form. It's a fundamental definition for logarithms and it
comes in quite handy for solving lots of logarithmic problems.
.

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