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Chapter 12: Problem 11

Write each equation in its equivalent logarithmic form. $$2^{-4}=\frac{1}{16}$$

Short Answer

Expert verified
The logarithmic form of the equation \(2^{-4}=\frac{1}{16}\) is \( \log_2 \left(\frac{1}{16}\right) = -4 \)

Step by step solution

01

Understand the logarithmic form

A logarithmic form is represented by \( \log_b (a) = n \), where \( b \) is the base, \( a \) is the result and \( n \) is the exponent.
02

Apply the logarithmic principle

Substitute the base, the result, and the exponent from the original exponential equation into the logarithmic form. The base in the exponential equation becomes the base in the logarithmic form. The exponent in the exponential form becomes the number that the logarithm equals in the logarithmic form. The result in the exponential form becomes the argument of the logarithm in the logarithmic form.
03

Write the equation in logarithmic form

Following the principles in Step 2, the base is 2, the result is 1/16 and the exponent is -4. So, the logarithmic form is \( \log_2 \left(\frac{1}{16}\right) = -4 \)

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Most popular questions from this chapter

Without using a calculator, find the exact value of \(\log _{4}\left[\log _{3}\left(\log _{2} 8\right)\right]\)

Solve each equation. $$5^{x^{2}-12}=25^{2 x}$$

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Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. When graphing a logarithmic function, I like to show the graph of its horizontal asymptote.

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