/*! 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 11 Evaluate each logarithm to four ... [FREE SOLUTION] | 91影视

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Chapter 12: Problem 11

Evaluate each logarithm to four decimal places. \(\log 43\)

Short Answer

Expert verified
1.6335

Step by step solution

01

Understand the Logarithm

The logarithm \(\text{log} \, 43\) asks for the exponent by which the base 10 must be raised to yield 43. Logarithms can be evaluated using scientific calculators for more precision.
02

Use a Calculator

Use a scientific calculator to evaluate \(\text{log} \, 43\). Ensure the calculator is set to the common logarithm (base 10) mode.
03

Calculate the Value

Enter 43 into the calculator and apply the 'log' function. The result should be approximately \(1.633468\).
04

Round to Four Decimal Places

Round the calculated logarithm value to four decimal places. \(1.633468\) rounded to four decimal places is \(1.6335\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Common Logarithm
Logarithms are a mathematical concept that determine how many times a base number must be multiplied by itself to produce another number. A common logarithm has a base of 10. For example, \(\text{log} \, 43\) asks for the power to which 10 must be raised to get 43. The notation typically used for common logarithms is \(\text{log}\) without specifying the base, as it is understood to be base 10. This concept is essential as it simplifies complex multiplicative processes into simpler additive ones. Common logarithms are widely used in various fields such as science, engineering, and finance.
Scientific Calculator
A scientific calculator is an advanced tool necessary for performing more complicated mathematical functions, including logarithms, exponents, and trigonometric functions. These calculators have a special button labeled 'log' that is used to calculate common logarithms. To evaluate \(\text{log} \, 43\), begin by turning on the calculator and ensuring it is set to the correct mode. Most scientific calculators default to base 10 for logarithms, so no additional settings are typically needed. Enter the number, in this case, 43, and then press the 'log' button. The display will show the logarithmic value, which should be approximately \(1.633468\).
Rounding to Four Decimal Places
Rounding numbers is a fundamental mathematical skill used to simplify figures while maintaining their relative accuracy. When we round the logarithmic value of \(1.633468\) to four decimal places, we need to consider the fifth decimal place. If the fifth decimal, in this case, 6, is 5 or greater, increase the fourth decimal place by one. Hence, \(1.633468\) becomes \(1.6335\). This level of precision ensures accuracy while making the number easier to work with. Always remember to follow the rounding rules to retain the integrity of your calculations.

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Most popular questions from this chapter

Use the properties of logarithms to express each logarithm as a sum or difference of logarithms, or as a single logarithm if possible. Assume that all variables represent positive real numbers. $$\log _{4} 6^{2}$$

Each of the following functions is one-to-one. Graph the function as a solid line (or curve), and then graph its inverse on the same set of axes as a dashed line (or curve). Complete any tables to help graph the functions. $$ f(x)=2 x+3 $$

Solve each equation. \(\log _{x} 9=\frac{1}{2}\)

Use the properties of logarithms to write each expression as a single logarithm. Assume that all variables are defined in such a way that the variable expressions are positive, and bases are positive numbers not equal to 1. $$\log _{10}(x+3)+\log _{10}(x+5)$$

Solve each equation. Use natural logarithms. Approximate solutions to three decimal places when appropriate. $$ e^{\ln 2 x}=e^{\ln (x+1)} $$
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