/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 37 Evaluate each expression without... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 37

Evaluate each expression without using a calculator. $$\log _{4} 1$$

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Step by step solution

01

Understanding the problem

Given expression is \( \log _{4} 1 \). The logarithm base 4 of 1 represents the power or exponent to which 4 must be raised to get 1.
02

Apply the logarithmic rule

One of the basic facts about logarithms is that any number (except 0) raised to the power of 0 equals 1. That is, if a^0 = 1, then log_a(1) = 0, where a is the base.
03

Evaluate the expression

Therefore, applying this rule to our expression, \( \log _{4} 1 \) is equal to 0.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because the equations $$\log (3 x+1)=5 \text { and } \log (3 x+1)=\log 5$$ are similar, I solved them using the same method.

Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution=set. Verify this value by direct substitution into the equation. $$3^{x}=2 x+3$$

The logistic growth function $$ P(x)=\frac{90}{1+271 e^{-0.122 x}} $$ models the percentage, \(P(x),\) of Americans who are \(x\) years old with some coronary heart disease. Use the function to solve Exercises \(43-46\) What percentage of 20 -year-olds have some coronary heart disease?

a. Simplify: \(e^{\ln 3}\) b. Use your simplification from part (a) to rewrite \(3^{x}\) in terms of base \(e\)

Exercises \(83-85\) will help you prepare for the material covered in the first section of the next chapter. a. Does \((4,-1)\) satisfy \(x+2 y=2 ?\) b. Does \((4,-1)\) satisfy \(x-2 y=6 ?\)
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