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Chapter 4: Problem 9

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. $$ \log \left(\frac{x}{100}\right) $$

Short Answer

Expert verified
The expansion of the given logarithmic expression \(\log \left(\frac{x}{100}\right)\) is \(\log(x) - 2\).

Step by step solution

01

Apply the Quotient Rule

To start with, the equation is written in logarithmic form as: \( \log \left(\frac{x}{100}\right) \)By applying the quotient rule, the equation becomes: \( \log(x) - \log(100) \)
02

Evaluate Logarithmic Expressions

We know that \(\log(100) = 2\) because \((10^2 = 100)\), hence, replace \(\log(100)\) by \(2\) in the equation. So the equation now is: \( \log(x) - 2 \)

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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. $$ 3 \ln x+5 \ln y-6 \ln z $$

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. $$ \log (3 x+7)-\log x $$

Solve each equation in Exercises \(89-91 .\) Check each proposed solution by direct substitution or with a graphing utility. $$\ln (\ln x)=0$$

Describe the power rule for logarithms and give an example.

Describe the quotient rule for logarithms and give an example.
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