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Chapter 4: Problem 19

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

Short Answer

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

Step by step solution

01

Identify the base of the exponent

The base of the exponent in the given equation is 7. This is represented as \(b\) in the general formula. So, \(b = 7\).
02

Identify the value of the exponent

The value of the exponent is \(y\), which is \(x\) in the general formula. So, \(x = y\).
03

Identify the result of the exponentiation

The result of exponentiation is 200. In the general formula this is represented as \(y\). So, \(y = 200\).
04

Write the logarithmic form

By inserting values into the general formula for converting an exponential form to a logarithmic form \(\log_{b}(y) = x\), the equivalent logarithmic form of the given exponential equation \(7^{y}=200\) is \(\log_{7}(200) = y\)

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Most popular questions from this chapter

Explain how to use the graph of \(f(x)=2^{x}\) to obtain the graph of \(g(x)=\log _{2} x\).

Explain how to find the domain of a logarithmic function.

Use the exponential growth model, \(A=A_{0} e^{k t},\) to show that the time it takes a population to double (to grow from \(A_{0}\) to \(\left.2 A_{0}\right)\) is given by \(t=\frac{\ln 2}{k}\)

Graph \(f\) and \(g\) in the same viewing rectangle. Then describe the relationship of the graph of g to the graph of \(f\). $$f(x)=\ln x, g(x)=\ln (x+3)$$

Exercises \(83-85\) will help you prepare for the material covered in the first section of the next chapter. Graph \(x+2 y=2\) and \(x-2 y=6\) in the same rectangular coordinate system. At what point do the graphs intersect?
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