Question 93117
The rule is as follows:
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{{{log(a,b) = y}}} is equivalent to {{{a^y = b}}}
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So in {{{log(2,16) = 4}}} a = 2, b = 16, and y = 4. Therefore, the equivalent exponential
form is {{{2^4 = 16}}}
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Your next problem has a typo or your source of the problem is trying to see if you can catch
the error. You are given that {{{log(2,125) = 3}}}. In this form a = 2, b = 125, and y = 3,
so the "equivalent" exponential form is {{{2^3 = 125}}}. But notice that this is not true.
The original problem should be {{{log(5,125) = 3}}}. The equivalent exponential form is
then {{{5^3 = 125}}} and this is true.
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Finally you are given the exponential form {{{10^(-1) = 0.1}}} and are asked to convert it
to logarithmic form. By comparing this given with the exponential rule, you can see that
a = 10, b = 0.1, and y = -1.  Substituting these into the logarithmic rule you get the
equivalent form {{{log(10, 0.1) = -1}}}.
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Hope this helps you to understand this conversion process.