SOLUTION: log base5 x=30 The value of x is? is it 15?

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Question 86946: log base5 x=30
The value of x is?
is it 15?

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
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Log%5B5%5Dx=30
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Solve for x
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You can convert this problem to exponential form to solve it. The conversion between
logarithmic and exponential form is done according to the following relationship:
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Log%5Bb%5DA+=+C is equivalent to the exponential form b%5EC+=+A
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Remember this relationship. It's quite useful in solving logarithmic problems.
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If you compare what you are given to the log form you can see that b = 5, C = 30, and A = x.
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Now substitute these values into the exponential form and you get:
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5%5E30+=+x
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So x+=+5%5E30 and that is a pretty big number. You can use a calculator to find that
5%5E30 is approximately 9.313225746%2A10%5E20
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These are answers that you are looking for. Let's work a similar problem with smaller numbers
just for practice. Suppose the problem had been:
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Log%5B5%5Dx+=+3
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You solve for x by converting this log form to exponential form. In this case b = 5,
C = 3, and A = x. Substituting these values into the exponential form results in:
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5%5E3+=+x
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and 5 cubed is 5*5*5 = 125. So for this problem, x would be 125, and you can now write:
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Log%5B5%5D125+=+3
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Hope this helps you to understand the problem a little better
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