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3 years ago

A.line CD B.line ED C.point C D.point D

Mathematics

1 answer:

Hunter-Best [27]3 years ago

4 0

I am confused what is your question then i will tell you the answer.

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If logb2=x and logb3=y, evaluate the following in terms of x and y:

Alja [10]

$log_b{162} = x + 4y\\\\log_b324 = 2x+4y\\\\log_b\frac{8}{9} = 3x-2y\\\\\frac{log_b27}{log_b16} = 3y-4x$

Solution:

Given that,

$log_b2 = x\\\\log_b3 = y --------(i)$

Use the following log rules

Rule 1: $log_b(ac) = log_ba + log_bc$

Rule 2: $log_b\frac{a}{c} = log_ba - log_bc$

Rule 3: $log_ba^c = clog_ba$

$a) log_b{162}$

Break 162 down to primes:

$162 = 2^1 \times 3^4$

$log_b{162} =log_b 2^1. 3^4\\\\By\ rule\ 1\\\\ log_b{162} = log_b 2^1 +log_b 3^4\\\\By\ rule\ 3\\\\1log_b2 + 4log_b3\\\\1x+4y\\\\x+4y$

Thus we get,

$log_b162 = x + 4y$

$b) log_b 324$

Break 324 down to primes:

$324 = 2^2 \times 3^4$

$log_b324 = log_b 2^2.3^4\\\\By\ rule\ 1\\\\log_b324 = log_b2^2 + log_b3^4\\\\By\ rule\ 3\\\\log_b324 = 2log_b2 + 4log_b3\\\\From\ (i)\\\\log_b324 = 2x + 4y$

$c) log_b\frac{8}{9}$

By rule 2

$log_b\frac{8}{9} = log_b8 - log_b9\\\\log_b\frac{8}{9} = log_b 2^3 - log_b3^2\\\\By\ rule\ 3\\\\log_b\frac{8}{9} = 3 log_b2 - 2log_b3\\\\From\ (i)\\\\log_b\frac{8}{9} = 3x - 2y$

$d) \frac{log_b27}{log_b16}$

By rule 2

$\frac{log_b27}{log_b16} = log_b27 - log_b16\\\\ \frac{log_b27}{log_b16} = log_b3^3 - log_b2^4\\\\By\ rule\ 2\\\\ \frac{log_b27}{log_b16} = 3log_b3 - 4log_b2 \\\\From\ (i)\\\\\frac{log_b27}{log_b16} = 3y - 4x$

Thus the given are evaluated in terms of x and y

3 0

3 years ago

A retail shop is replacing their flooring with laminate wood. The floor plan is shown below. Determine the total square feet of

almond37 [142]

Answer:

1075 ft

Step-by-step explanation:

25*35 = 875

8*25 = 200

875+200 = 1075

3 0

3 years ago

Find the slope between the points ( 14 17) and (19, - 8).

ale4655 [162]

-5 because when using the slope intercept formula n plug in the x n y values u get -5

7 0

3 years ago

Read 2 more answers

Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = -2x3 + 4x2 - 2x + 8

Scorpion4ik [409]

Rational zero theorem is all combinations of p(factors of the constant) divided by q(factors of the first coefficient)

factors of 8 are 1, 2, 4, 8
factors of 2 are 1, 2

so all possible rational zeros are all combinations of p/q

+/- 1/1, 1/2, 2/1, 2/2, 4/1, 4/2, 8/1, 8/2

Now there are some repeats in there so you have to leave those out and once we do that we get

+/- 1, 1/2, 2, 4, 8

Remember all those are plus OR minus

6 0

3 years ago

Find the solution of this system of equations -x-4y=37 -2x-4y=-53

Lelu [443]

Answer:

Final answer is x=90, $y=-\frac{127}{4}$

Step-by-step explanation:

Given equations are:

-x-4y=37 ...(i)

-2x-4y=-53 ...(ii)

multiply (ii) by -1

2x+4y=53 ...(iii)

Add (i) and (iii)

x=90

plug value of x=90 into (i)

-x-4y=37

-90-4y=37

-4y=37+90

-4y=127

$y=-\frac{127}{4}$

Hence final answer is x=90, $y=-\frac{127}{4}$

5 0

4 years ago

Read 2 more answers