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mezya [45]
3 years ago
11

Suppose log subscript a x equals 3, log subscript a y equals 7, and log subscript a z equals short dash 2. Find the value of the

following expression. log subscript a open parentheses fraction numerator x cubed y over denominator z to the power of 4 end fraction close parentheses
Mathematics
1 answer:
enyata [817]3 years ago
6 0

Answer:

<h2>24</h2>

Step-by-step explanation:

Given the following logarithmic expressions log_ax = 3, log_ay = 7, log_az = -2, we are to find the value of log_a(\frac{x^3y}{z^4} )

from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}Substituting x = a³, y = a⁷ and z = a⁻² into the log function log_a(\frac{x^3y}{z^4} ) we will have;

= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24

Hence, the value of the logarithm expression is 24

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Step-by-step explanation:

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1. Is triangle P’Q’R larger or smaller than triangle PQR? Explain how you know
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The length of the line is PQ as this line is parallel to the x - axis. So, the length of the line is the summation of 10 from second quadrant and 20 from first quadrant. So, the sum is 30. Hence the length of the line is 30 units.

Step-by-step explanation:

The length of a line segment can be measured by measuring the distance between its two endpoints. It is the path between the two points with a definite length that can be measured. Explanation: On a graph, the length of a line segment can be found by using the distance formula between its endpoints.

7 0
2 years ago
From a hot-air balloon, Juan measures a 36° angle of depression to a landmark that's
Masja [62]

Using the slope concept, it is found that the balloon's vertical distance above the ground is of 437.4 feet.

<h3>What is a slope?</h3>

The slope is given by the <u>vertical change divided by the horizontal change</u>, and it's also the tangent of the angle of depression.

In this problem:

  • The vertical change is x.
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Hence, applying the concept:

tan (36º) = x/602

x = 602 x tan(36º)

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More can be learned about the slope concept at brainly.com/question/18090623

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James knows that when he walks, he takes about 120
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Answer:

speed of James is: 3.75 miles/hour.

Step-by-step explanation:

We need to find the speed of James in miles per hour(mi/hr)

we know that 1 mile=5280 feet

James takes 120 steps in 1 minute so he will cover 120×60 steps in 1 hour.

i.e. he takes 7200 steps in 1 hour.

also each step of James=2.75 feet

total distance covered by James in 1 hour=2.75×7200 feet=19800 feet

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hence speed of James= (distance covered by james in 1 hour)/1 hour

speed of James=3.75 miles/hour.

Thanks!!

Mark me brainliest!

~FieryAnswererGT~

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