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Chapter 4: Problem 36

Evaluate each expression without using a calculator. $$\log _{11} 11$$

Short Answer

Expert verified
The value of the expression \( \log_{11} {11} \) is 1.

Step by step solution

01

Recognize properties of logarithms

The logarithm of a number in the same base is always equal to 1. This is because the logarithm of a number x to the base b is the power to which we must raise b to obtain x. In this case, we have \( \log_{11} {11} \). Here, the base and the number are the same, which means that the power to which we must raise 11 to get 11 is just 1.
02

Simplify the expression

So, \( \log_{11} {11} = 1 \). Hence, the value of the given expression is 1 without using a calculator.

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Most popular questions from this chapter

Research applications of logarithmic functions as mathematical models and plan a seminar based on your group's research. Each group member should research one of the following areas or any other area of interest: \(\mathrm{pH}\) (acidity of solutions), intensity of sound (decibels), brightness of stars, human memory, progress over time in a sport, profit over time. For the area that you select, explain how logarithmic functions are used and provide examples.

Evaluate or simplify each expression without using a calculator. $$ \ln \frac{1}{e^{7}} $$

The function \(P(t)=145 e^{-0.092 t}\) models a runner's pulse, \(P(t),\) in beats per minute, \(t\) minutes after a race, where \(0 \leq t \leq 15 .\) Graph the function using a graphing utility. TRACE along the graph and determine after how many minutes the runner's pulse will be 70 beats per minute. Round to the nearest tenth of a minute. Verify your observation algebraically.

Evaluate each expression without using a calculator. $$ \log _{2}\left(\log _{3} 81\right) $$

Evaluate or simplify each expression without using a calculator. $$ \ln e^{7} $$
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