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Chapter 4: Problem 61

Evaluate each expression without using a calculator. $$\log 100$$

Short Answer

Expert verified
The value of \(\log 100\) is 2.

Step by step solution

01

Understanding the question

The operation to be performed is \(\log 100\). This is a common logarithm and therefore, the base is 10. The question requires finding the power to which 10 must be raised to get 100.
02

Applying the logarithm rule

Remember that \(\log_b a = n\) is equivalent to \(b^n = a\). In this case, the question is asking to solve the equation \(10^n = 100\). Which value of \(n\) makes this equation true?
03

Finding the solution

Knowing that \(10^2 = 100\), it is clear that the value of \(n\) which satisfies the equation is 2. Therefore, \(\log 100 = 2\).

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Most popular questions from this chapter

In Exercises \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ 3 \ln x+5 \ln y-6 \ln z $$

Find \(\ln 2\) using a calculator. Then calculate each of the following: \(1-\frac{1}{2} ; 1-\frac{1}{2}+\frac{1}{3} ; 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\) \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5} ; \ldots .\) Describe what you observe.

In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$ \log _{b}\left(\frac{V x y^{3}}{z^{3}}\right) $$

In Exercises \(79-82,\) use a graphing utility and the change-of- base property to graph each function. $$ y=\log _{3}(x-2) $$

In Exercises \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ \log _{2} 96-\log _{2} 3 $$
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