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2 years ago

10

What is the greatest common denominator of 81, 108, and 117?

1 answer:

stira [4]2 years ago

8 0

If you mean greatest common factor then that means

factor each and group the ones that are same

81=3 times 3 times 3 times 3
108=2 times 2 times 3 times 3 times 3
117=3 times 3 times 13
so we look for the group common to all (I bolded it)

81=3 times 3 times 3 times 3
108=2 times 2 times 3 times 3 times 3
117=3 times 3 times 13
the answeis 3 times 3=9

greates common denomenator of these nubers is 9

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<u><em>The satisfied table of the given function</em></u> $y = log_{b} (x)$ <u><em></em></u>

<em>x 1/8 1/4 1/2 1 2</em>

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<em></em>

Step-by-step explanation:

<u><em>Explanation</em></u> :-

Given logarithmic function $y = log_{b} (x)$ if b >1

Given first table

i)

put x = $\frac{1}{8}$ given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{8} )$

$y = log_{2} (2^{-3} )$

we will apply logarithmic formula

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$y = log_{2} (2^{-3} ) = -3 log_{2} (2) = -3 (1) = -3$

<em>y = -3</em>

<em>ii)</em>

<em>put x = </em> $\frac{1}{4}$ <em> given b > 1 so we can choose b = 2</em>

<em></em> $y = log_{2} (\frac{1}{4} )$ <em></em>

<em></em> $y = log_{2} (2^{-2} )$ <em></em>

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-2} ) = -2 log_{2} (2) = -2 (1) = -2$

<em>y = -2</em>

<em>iii) </em>

<em>put x = </em> $\frac{1}{2}$ <em> given b > 1 so we can choose b = 2</em>

<em></em> $y = log_{2} (\frac{1}{2} )$ <em></em>

$y = log_{2} (2^{-1} )$

<em>we will apply logarithmic formula </em>

<em>log x ⁿ = n log (x)</em>

$y = log_{2} (2^{-1} ) = -1 log_{2} (2) = - (1) = -1$

<em>y = -1</em>

<em>iv) </em>

<em>put x = 1 given b > 1 so we can choose b = 2</em>

<em></em> $y = log_{2} (1 )$ <em> = 0</em>

<em>y = 0</em>

<em>v) </em>

<em>put x = </em> $2$ <em> given b > 1 so we can choose b = 2</em>

$y = log_{2} (2 )$

<em>y = 1</em>

<em></em>

<u><em>Final answer:-</em></u>

<u><em>The satisfied table of the given function</em></u>

<em>x 1/8 1/4 1/2 1 2</em>

<em>y -3 -2 -1 0 1</em>

<em></em>

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