Explain how you would know log3100 is between 4 and 5 without the use of a calculator.

1 answer:

6 0

$\log{3100}=\log{(100\times 31)}=\log{100}+\log{31}=\log{10^2}+\log{31}=
\\ =2\log{10}+\log{31}=2\times1+\log{31}=2+\log{31}
\\
\\ 2+\log{10}\ \textless \ 2+\log{31}\ \textless \ 2+\log{100}
\\ 2+\log{10}\ \textless \ 2+\log{31}\ \textless \ 2+\log{10^2}
\\ 2+\log{10}\ \textless \ 2+\log{31}\ \textless \ 2+2\log{10}
\\ 2+1\ \textless \ 2+\log{31}\ \textless \ 2+2\times 1
\\ 3\ \textless \ 2+\log{31}\ \textless \ 4$

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Describe in words where the square root of twenty-four would be plotted on the number line.

Rzqust [24]

The square root of 24 would be plotted between 4 and 5, but closer to 5 on a number line.

<h3>What is a number line?</h3>

A number line is a horizontal line with evenly spaced numerical increments. The numbers on the line will dictate how you answer the number on the line.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, denoted by \mathbb {R}. Every point on a number line is assumed to be a real number, and every real number is assumed to be a point.

Number lines are extremely adaptable, that can be used to locate numbers, compare numbers, fractions and mixed numbers, decimals, integers, absolute value, addition, subtraction, inequalities, multiples, common denominators, and much more.

The square root of $\sqrt{24}=4.899$ , which is between 4 and 5, but closer to 5 on a number line.