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3 years ago

In a theater there are 15 chairs in the first row, each row has 3 more chairs than the previous

Mathematics

1 answer:

andrew11 [14]3 years ago

5 0

Answer:663

Step-by-step explanation:

The first row is 15,so you have to add three from the first row you and you get 18 and then you keep going and going till you get to the 17th row then you add the numbers together.

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The logarithm of a number to the base V2 is k. What is its logarithm to the base 2v2 ?

kakasveta [241]

Answer:

$log_{2\sqrt 2} X = \frac{1}{3}k$

Step-by-step explanation:

Given

Let the number be X

From the first statement, we have:

$log_{\sqrt 2} X = k$

Required

Find $log_{2\sqrt 2} X$

$log_{\sqrt 2} X = k$

using the following law of logarithm

$log_ab = n, b=a^n$

So:

$log_{\sqrt 2} X = k$

$X = \sqrt{2}^k$

Substitute: $X = \sqrt{2}^k$ in $log_{2\sqrt 2} X$

$log_{2\sqrt 2} X = log_{2\sqrt 2} ( \sqrt{2}^k)$

$log_{2\sqrt 2} X = klog_{2\sqrt 2} \sqrt{2}$

Apply the following law:

$log_ab = \frac{log\ b}{log\ a}$

$log_{2\sqrt 2} X = k\frac{log\ \sqrt 2}{log\ {2\sqrt 2}}$

Express the square roots as power

$log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2 * 2^\frac{1}{2}}}$

$log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2^\frac{3}{2}}}$

using the following law of logarithm

$log_ab = n, b=a^n$

$log_{2\sqrt 2} X = k\frac{\frac{1}{2}log\ 2}{\frac{3}{2}log\ 2}}$

$log_{2\sqrt 2} X = k\frac{\frac{1}{2}}{\frac{3}{2}}}$

Rewrite as:

$log_{2\sqrt 2} X = k * \frac{1}{2} \div\frac{3}{2}$

$log_{2\sqrt 2} X = k * \frac{1}{2} *\frac{2}{3}$

$log_{2\sqrt 2} X = k * \frac{1}{1} *\frac{1}{3}$

$log_{2\sqrt 2} X = \frac{1}{3}k$

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