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# Log question

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How would you solve log_2 (x/y) = 3?

Guest Mar 5, 2017
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#1
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log_2 (x/y) = 3?

y = x/8 = (log(x/y))/(log(2)) = 3 = log(x/y) = log(8) = log((8 y)/x) = 0

Guest Mar 5, 2017
#2
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Using the change of base formula:

$$\log_{2}(x/y) = \frac{log_{10}(x/y)}{\log_{10}2} = 3 \\~\\ \log_{10}(x/y)=3(\log_{10}2) \\~\\ \log_{10}(x/y)=\log_{10}(2^3) \\~\\ x/y = 2^3 \\~\\ x/y = 8$$

So x = 8y    and     y = x/8

I don't know what Guest did, but I'm pretty sure y can't be zero because that would make a zero in the denominator and that would mean that it doesn't equal 3, it would just not be a true statement.

hectictar  Mar 5, 2017

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