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Chapter 3: Problem 19

Find a number \(y\) such that \(\log _{2} y=-5\).

Short Answer

Expert verified
The value of \(y\) is \(\frac{1}{32}\).

Step by step solution

01

Understand the logarithm equation

We are given the logarithmic equation: \(\log _{2} y=-5\). Here, the base of the logarithm is 2, and we want to find the value of \(y\) when the logarithm is equal to -5.
02

Convert the logarithm equation into an exponential form

To convert the given logarithmic equation into an exponential form, we'll use the property of logarithms that states: \(\log _{b} a=c\) is equivalent to \(b^c=a\). Therefore, our equation becomes: \(2^{-5}=y\).
03

Calculate the value of y

Now, we just need to calculate the value of \(y\) by evaluating the expression \(2^{-5}\). This means we need to find the reciprocal of \(2^5\) which is: \(\frac{1}{2^5} = \frac{1}{32}\). So, the value of \(y\) is \(\frac{1}{32}\).

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