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3 years ago

Fully condense the expression. Assume that all variables represent positive numbers. (log x -2 log y+ 3 log z) (10 points)

Mathematics

1 answer:

AfilCa [17]3 years ago

5 0

Answer: The required condensed expression is $\log\dfrac{xz^3}{y^2}.$

Step-by-step explanation: We are given to fully condense the following logarithmic expression assuming that all variables represent positive numbers :

$E=\log x-2\log y+3\log z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following properties of logarithms :

$(i)~\log a^b=b\log a,\\\\(ii)~\log a+\log b=\log(ab),\\\\(iii)~\log a-\log b=\log\dfrac{a}{b}.$

Therefore, from expression (i), we get

$E\\\\=\log x-2\log y+3\log z\\\\=\log x-\log y^2+\log z^3\\\\=\log(xz^3)-\log y^2\\\\=\log\dfrac{xz^3}{y^2}.$

Thus, the required condensed expression is $\log\dfrac{xz^3}{y^2}.$

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4 years ago

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3 years ago

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Montano1993 [528]

<h2>Hello!</h2>

The answer is: $y=cscx$

Domain and range of trigonometric functions are already calculated, so let's discard one by one in order to find the correct answer.

The range is where the function can exist in the vertical axis when we assign values to the variable.

First:

$y=cosx$ : Incorrect, it does include 0.4 since the cosine range goes from -1 to 1 (-1 ≤ y ≤ 1)

Second:

$y=cotx$ : Incorrect, it also does include 0.4 since the cotangent range goes from is all the real numbers.

Third:

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Fourth:

$y=sinx$ : Incorrect, the sine function range is equal to the cosine function range (-1 ≤ y ≤ 1).

I attached a pic of the csc function graphic where you can verify the answer!

Have a nice day!

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