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Question 7(Multiple Choice)
(05.02 MC)
Which expression is equivalent to 3 log2 x - 4 log2 y + 2 log2 z?

Question 7Multiple Choice 0502 MC Which Expression Is Equivalent To 3 Log2 X 4 Log2 Y 2 Log2 Z class=

Answer :

CRYSTALQUEENGO

Answer:

C.) [tex]log_2(\frac{x^3z^2}{y^4})[/tex]

Step-by-step explanation:

To find the answer, you need to simplify the expression. To do so, you must combine the logs. You can combine the logs because they all have the same subscript (2).

[tex]3 log_2x - 4log_2y + 2log_2z[/tex]                           <----- Given expression

[tex]log_2x^3-log_2y^4+log_2z^2[/tex]                            <----- Raise coefficients to variables

[tex]log_2x^3+log_2z^2-log_2y^4[/tex]                            <----- Rearrange

[tex]log_2(x^3z^2)-log_2y^4[/tex]                                    <----- Multiply added logs

[tex]log_2(\frac{x^3z^2}{y^4})[/tex]                                                  <------ Divide subtracted log

SKANDARGO

3 ㏒₂ x - 4 ㏒₂ y + 2 ㏒₂ z

Express the multiplication of a logarithm number of an expression as the logarithm of the power of the expression.

㏒₂ x³ - ㏒₂ y⁴ + ㏒₂ z²

Take the product of the arguments

                         [tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ Log_{2} \frac{x^{3}z^{2} }{y^{4} } } }}}}[/tex]

Therefore, the correct option is alternative "C".

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