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Nitella [24]
3 years ago
14

Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that

can be evaluated without a calculator. log3(135x+81y)
Mathematics
1 answer:
Lorico [155]3 years ago
6 0

Answer:

\mathbf{1 +  log_3 ( 45x + 27y)}

Step-by-step explanation:

Given that:

log_3 (135x + 81 y) \\ \\  = log_3 [ 3 (45x + 27y) ]

Since log (ab) = log \  a +log  \ b

Then

log_3 [ 3 (45x + 27y) ] = log_3 (3) + log_3 ( 45x + 27y)

Since log_a (a) = 1

Then

log_3 (3) + log_3 ( 45 + 27y) = 1 +  log_3 ( 45x + 27y)

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9.45

Step-by-step explanation:

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Convert the measurement as indicated.<br><br> 26ft= _ yd _ ft
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26ft(yd/3ft)

8yd+2yd/3

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Solve 4 cos2x-3 = 0 for all real values of x.
vichka [17]

4 cos² x - 3 = 0

4 cos² x = 3

cos² x = 3/4

cos x = ±(√3)/2

Fixing the squared cosine doesn't discriminate among quadrants.  There's one in every quadrant

cos x = ± cos(π/6)

Let's do plus first.  In general, cos x = cos a has solutions x = ±a + 2πk integer k

cos x = cos(π/6)

x = ±π/6 + 2πk

Minus next.

cos x = -cos(π/6)

cos x = cos(π - π/6)

cos x = cos(5π/6)

x = ±5π/6 + 2πk

We'll write all our solutions as

x = { -5π/6, -π/6, π/6, 5π/6 } + 2πk integer k

3 0
3 years ago
The slope between A and B is 3/5.The slope between points B and C is 6/10.Antoine says all three of these points are on the same
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Suppose your professor reports that across all of her classes over the past 10 years, she found a -0.63 correlation between numb
Aleonysh [2.5K]

Using correlation coefficients, it is found that the -0.63 correlation between number of absences and final exam score means that there is a strong negative correlation between number of absences and final exam score.

<h3>What is a correlation coefficient?</h3>

It is an index that measures correlation between two variables, assuming values between -1 and 1.

If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.

In this problem, the correlation is of -0.63, hence:

It means that that there is a strong negative correlation between number of absences and final exam score.

To learn more about correlation coefficients, you can take a look at brainly.com/question/25815006

4 0
2 years ago
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