Question 86946
Given:
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{{{Log[5]x=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[b]A = C}}} is equivalent to the exponential form {{{b^C = 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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{{{5^30 = x}}}
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So {{{x = 5^30}}} and that is a pretty big number. You can use a calculator to find that
{{{5^30}}} is approximately {{{9.313225746*10^20}}}
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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[5]x = 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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{{{5^3 = 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[5]125 = 3}}}
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Hope this helps you to understand the problem a little better
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