Question

Question 7(Multiple Choice)

Answer 1

Answer:

C.) $log_2(\frac{x^3z^2}{y^4})$

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).

$3 log_2x - 4log_2y + 2log_2z$                           <----- Given expression

$log_2x^3-log_2y^4+log_2z^2$                            <----- Raise coefficients to variables

$log_2x^3+log_2z^2-log_2y^4$                            <----- Rearrange

$log_2(x^3z^2)-log_2y^4$                                    <----- Multiply added logs

$log_2(\frac{x^3z^2}{y^4})$                                                  <------ Divide subtracted log

Answer 2

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

                         $\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ Log_{2} \frac{x^{3}z^{2} }{y^{4} } } }}}}$

Therefore, the correct option is alternative "C".