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Problem 753

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

Expert verified
The value of $$N$$ is 4.
See the step by step solution

## 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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