Problem 77
Question
Evaluate each expression without using a calculator. $$\log _{3}\left(\log _{7} 7\right)$$
Step-by-Step Solution
Verified Answer
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1Step 1: Evaluate the Inner Logarithm
The first task is to simplify the expression \(\log _{7} 7\). Because the base of the logarithm and the number are the same (both 7), we can apply the property of logarithms that \(\log_b b = 1\). Thus, \(\log _{7} 7 = 1\).
2Step 2: Evaluate the Outer Logarithm
Now, we evaluate the outer logarithm using the result from Step 1. The expression \(\log _{3}(1)\) is the logarithm base 3 of 1. Since any number to the power of 0 is 1, we have that \(\log _{3}(1) = 0\).
Other exercises in this chapter
Problem 76
Write each equation in its equivalent exponential form. Then solve for \(x .\) $$\log _{64} x=\frac{2}{3}$$
View solution Problem 76
Solve each logarithmic equation. Be sure to reject any value of \(x\) that is not in the domain of the original logarithmic expressions. Give the exact answer.
View solution Problem 77
Determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s)
View solution Problem 78
Evaluate each expression without using a calculator. $$\log _{5}\left(\log _{2} 32\right)$$
View solution