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Problem 750

# If $$\log _{3} \mathrm{~N}=2$$, find $$\mathrm{N}$$

Expert verified
The short answer is: $$N = 9$$.
See the step by step solution

## 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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