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Chapter 12: Problem 19

Write each equation in its equivalent logarithmic form. $$7^{y}=200$$

Short Answer

Expert verified
The logarithmic form of the equation \(7^{y}=200\) is \(\log_{7}(200) = y\).

Step by step solution

01

Identify the variables

In the given equation \(7^{y}=200\), 7 is the base \(b\), y is the exponent and 200 is the argument \(x\).
02

Convert to Logarithmic form

Use the conversion rule to write the equation in logarithmic form. The base of the logarithm is the base of the exponential, the argument of the logarithm is the the number on the other side of the equation and the result of the logarithm is the power of the exponential. Therefore, the equivalent logarithmic form of the equation \(7^{y}=200\) is \(\log_{7}(200) = y\).

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Most popular questions from this chapter

Without using a calculator, find the exact value of $$\frac{\log _{3} 81-\log _{\pi} 1}{\log _{2 \sqrt{2}} 8-\log 0.001}$$

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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.

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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