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Chapter 26: Chapter 26

Problem 753

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Find the value of \(\mathrm{N}\) if \(\log _{8} \mathrm{~N}=2 / 3\).

Short Answer

Expert verified
The value of \(N\) is 4.
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Write down the given equation

Write down the given equation: \(\log_{8}{N}=\frac{2}{3}\).

Step 2: Convert to exponential form

Using the definition of logarithms, we can convert the logarithmic form of the equation into its exponential form: \(8^{\frac{2}{3}}=N\).

Step 3: Calculate the value of N

Now, we just need to calculate the value of the expression on the left side of the equation: \(N=8^{\frac{2}{3}}=(8^{\frac{1}{3}})^2\) Since \(8^{\frac{1}{3}}\) refers to the cube root of 8, and the cube root of 8 is 2, we can simplify the equation: \(N=(2)^2 = 4\) So, the value of \(N\) is 4.

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