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Chapter 26: Chapter 26

Problem 750

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If \(\log _{3} \mathrm{~N}=2\), find \(\mathrm{N}\)

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The short answer is: \(N = 9\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: 1. Write the logarithmic equation in exponential form

To convert the logarithmic form \(\log_{3} N = 2\) to its exponential form, we can use the rule: \(a^{\log_{a} b}=b\). Here, the base \(a\) is 3, so we have \(3^{\log_{3} N}=N\). Now we can rewrite the given equation as: \[3^2 = N\]

Step 2: 2. Solve for N

Now that we have the exponential equation \[3^2 = N\], we can calculate the value of \(N\). We know that \(3^2\) is equal to 9, so we have: \[N = 9\] Thus, the value of \(\boldsymbol{N}\) is \(\boldsymbol{9}\).

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