Question

Question 7(Multiple Choice)

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

Answer 1

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) (x^(3)z^(2) )/(y^(4) ) } }}}}`

Therefore, the correct option is alternative "C".

Answer 2

C.)
`log_2((x^3z^2)/(y^4))`

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((x^3z^2)/(y^4))` <------ Divide subtracted log