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Problem 10

# Express each equation in logarithmic form. $$16^{-1 / 4}=0.5$$

Expert verified
The logarithmic form of the given equation is $$\log_{16}(0.5) = -\frac{1}{4}$$.
See the step by step solution

## Step 1: Identify the Base, Exponent, and Result

In the given equation $$16^{-1 / 4}=0.5$$, the base is 16, the exponent is $$-1/4$$, and the result is 0.5.

## Step 2: Apply the Logarithmic Form

According to the logarithmic form, we can rewrite the equation as: $$\log_{base}(result) = exponent$$ So, we will replace the base, exponent, and result with their corresponding values.

## Step 3: Rewrite the Equation in Logarithmic Form

Using the values from the given equation, our logarithmic equation becomes: $$\log_{16}(0.5) = -\frac{1}{4}$$ So, the logarithmic form of the given equation is $$\log_{16}(0.5) = -\frac{1}{4}$$.

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