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Chapter 12: Problem 2

Write each equation in its equivalent exponential form. $$6=\log _{2} 64$$

Short Answer

Expert verified
The equivalent exponential form of the equation \(6=\log _{2} 64\) is \(2^6 = 64\).

Step by step solution

01

Identify the elements of the logarithmic equation

The base of logarithm is 2. 6 is the logarithm of 64 to the base 2, it can be denoted as \(\log _{2} 64 = 6\). Thus, the base is 2, the 'result' a is 64, and the logarithm c is 6.
02

Apply the formula for converting logarithmic form to exponential form

We will use the formula \(b^c = a\), where b is the base, c is the power (or logarithm) and a is the result. Substituting the identified elements into the formula, b is 2, c is 6 and a is 64.
03

Write down the equivalent exponential form

Following the conversion formula from Step 2, the equivalent exponential form of the given logarithmic equation \(\log _{2} 64 = 6\) becomes \(2^6 = 64\).

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Most popular questions from this chapter

Graph: \(5 x-2 y>10\)

a. Use a graphing utility (and the change-of-base property) to graph \(y=\log _{3} x\) b. Graph \(\quad y=2+\log _{3} x, \quad y=\log _{3}(x+2), \quad\) and \(y=-\log _{3} x \quad\) in the same viewing rectangle as \(y=\log _{3} x .\) Then describe the change or changes that need to be made to the graph of \(y=\log _{3} x\) to obtain each of these three graphs.

Explain how to find the domain of a logarithmic function.

Explain the differences between solving \(\log _{3}(x-1)=4\) and \(\log _{3}(x-1)=\log _{3} 4\).

The formula \(A=36.1 e^{0.0126 t}\) models the population of California, \(A,\) in millions, \(t\) years after 2005 a. What was the population of California in \(2005 ?\) b. When will the population of California reach 40 million?
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