Between what two consecutive integers must log2(17) lie

Mathematics

1 answer:

miss Akunina [59]2 years ago

3 0

Answer:

4 and 5

Step-by-step explanation:

For answering questions like this, it can be useful to remember a few of the powers of small integers:

2^4 = 16

2^5 = 32

<h3>Exponents and logarithms</h3>

A logarithm can be considered to be an exponent of the base.

$\log_b(x) = a \ \Longleftrightarrow\ b^a=x$

The ordering of powers of 2 relative to the number of interest (17) is ...

16 < 17 < 32

2⁴ < 17 < 2⁵ . . . . . . . . . . . . . . . . . . . expressed as powers of 2

log₂(2⁴) < log₂(17) < log₂(2⁵) . . . . . log₂ of the above inequality

4 < log₂(17) < 5 . . . . . . . . . . . . . . . . showing the values of the logs

Log₂(17) lies between 4 and 5.

<em>Additional comment</em>

Using the "change of base" formula, you can use a calculator to find the value of log₂(17). It shows you the value is between 4 and 5.

log₂(17) = log(17)/log(2) . . . . . . using logs to the same base

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What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer. Law of sines: answers

Dominik [7]

Answer:

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Step-by-step explanation:

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$\begin{array}{rcl}A + B + C & = & 180^{\circ}\\66^{\circ} + 76^{\circ} + C & = & 180^{\circ}\\142^{\circ} + C & = & 180^{\circ}\\C & = & 38\, ^{\circ}\\\end{array}$

2. Calculate b

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$\begin{array}{rcl}\dfrac{b}{\sin B } & = & \dfrac{c}{\sin C}\\\\\dfrac{b}{\sin 76^{\circ}} & = & \dfrac{3}{\sin 38^{\circ}}\\\\\dfrac{b}{0.9703} & = & \dfrac{3}{0.6157}\\\\ & = & 4.873\\b & = & 0.9703\times 4.873\\& = & \boxed{\mathbf{4.7}}\\\end{array}$