Problem 27
Question
Evaluate each expression without using a calculator. $$\log _{2} \frac{1}{8}$$
Step-by-Step Solution
Verified Answer
-3
1Step 1: Apply logarithm properties
Use the product rule \(\log(ab) = \log a + \log b\), quotient rule \(\log(a/b) = \log a - \log b\), and power rule \(\log(a^n) = n\log a\).
2Step 2: Simplify
The result is -3.
Other exercises in this chapter
Problem 27
Begin by graphing \(f(x)=2^{x}\). Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use
View solution Problem 27
Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
View solution Problem 28
Use the exponential decay model, \(A=A_{0} e^{k t},\) to solve Exercises \(28-31 .\) Round answers to one decimal place. The half-life of thorium-229 is 7340 ye
View solution Problem 28
Solve each exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approxi
View solution