Problem 17
Question
Write each equation in its equivalent logarithmic form. $$b^{3}=1000$$
Step-by-Step Solution
Verified Answer
The logarithmic form of the equation \(b^{3}=1000\) is \(\log_b(1000) = 3\).
1Step 1: Identify the base, exponent, and result of the exponential equation
The equation \(b^{3}=1000\) has base \(b\), exponent \(3\), and result \(1000\).
2Step 2: Apply the definition of logarithm to re-write the equation
The definition of a logarithm tells us that we can rewrite the equation \(b^{3}=1000\) in logarithmic form as \(\log_b(1000) = 3\).
Other exercises in this chapter
Problem 17
In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions
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Solve each exponential equation in Exercises \(1-26\) Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approxi
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Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. \(f(x)=(0.6)^{x}\)
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In Exercises \(1-40,\) use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions
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