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Chapter 3: Problem 17

Find a number \(y\) such that \(\log _{2} y=7\).

Short Answer

Expert verified
The value of \(y\) that satisfies \(\log_{2} y = 7\) is \(y = 128\).

Step by step solution

01

Rewrite the equation in exponential form

To convert the equation \(\log_{2} y = 7\) to exponential form, we'll use the property that \(\log_{b} x = n\) is equivalent to \(b^n = x\). Therefore, we rewrite the given equation as: \[ 2^7 = y \]
02

Evaluate \(2^7\)

Now we'll find the value of \(2^7\). This means multiplying \(2\) by itself \(7\) times: \[ 2^7 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 128 \]
03

Write the solution

Since we now know that \(2^7 = 128\), we can substitute this value back into the equation we found in Step 1: \[ y = 128 \] Thus, the value of \(y\) that satisfies \(\log_{2} y = 7\) is \(y = 128\).

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