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Chapter 4: Problem 15

Write each equation in its equivalent logarithmic form. $$13^{2}=x$$

Short Answer

Expert verified
The logarithmic form of the expression \(13^{2} = x\) is \(\log_{13}(x) = 2\).

Step by step solution

01

Identify the Base, Exponent and Result

In the given exponential expression \(13^{2} = x\), understand that '13' is the base, '2' is the exponent, and 'x' is the result.
02

Convert to Logarithmic Form

Using the logarithmic conversion formula, \(b^{y} = z\) can be rewritten as \(\log_{b}(z) = y\). This simply means 'log base b of z equals y'. Thus the exponential equation \(13^{2} = x\) can be expressed in logarithmic form as \(\log_{13}(x) = 2\).

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Most popular questions from this chapter

Complete the table for a savings account subject to contimuous compounding ( \(A=P e^{n}\) ). Round answers to one decimal place. Amount Invested 8000 dollar Annual Interest Rate 8% Accumulated Amount Double the amount invested Time \(t\) in Years _______

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Students in a psychology class took a final examination. As part of an experiment to see how much of the course content they remembered over time, they took equivalent forms of the exam in monthly intervals thereafter. The average score for the group, \(f(t),\) after \(t\) months was modeled by the function $$f(t)=88-15 \ln (t+1), \quad 0 \leq t \leq 12$$ a. What was the average score on the original exam? b. What was the average score after 2 months? 4 months? 6 months? 8 months? 10 months? one year? c. Sketch the graph of \(f\) (either by hand or with a graphing utility). Describe what the graph indicates in terms of the material retained by the students.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(\log _{b} x\) is the exponent to which \(b\) must be raised to obtain \(x\).

In parts (a)-(c), graph \(f\) and \(g\) in the same viewing rectangle. a. \(f(x)=\ln (3 x), g(x)=\ln 3+\ln x\) b. \(f(x)=\log \left(5 x^{2}\right), g(x)=\log 5+\log x^{2}\) c. \(f(x)=\ln \left(2 x^{3}\right), g(x)=\ln 2+\ln x^{3}\) d. Describe what you observe in parts (a)-(c). Generalize this observation by writing an equivalent expression for \(\log _{b}(M N),\) where \(M>0\) and \(N>0\) e. Complete this statement: The logarithm of a product is equal to _________.
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