Question

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms.

log base two of quantity x to the ninth power times y to the fifth power divided by eight.


nine times log base two of x minus five times log base two of y minus log base two of eight.

nine times log base two of x plus five times log base two of y minus log base two of eight.

nine times log base two of x times five times log base two of y minus log base two of eight.

nine times log base two of x plus five times log base two of y plus log base two of eight.

Answer 1

Choice B.

Explanation:

log2 [ x^9 * (y^5) /8]

= log2 x^9 + log2 y^5 - log2 8

= 9 log2 x + 5 log2 y - log2 8

That is choice B.

Answer 2

nine times log base two of x plus five times log base two of y minus log base two of eight i.e 9
`log_(2)` x + 5
`log_(2)` y -
`log_(2)` 8.

Explanation:

The question can be expressed mathematically as thus:

`log_(2)` [(
`x^(9)` ×
`y^(5)` ) ÷ 8]

=
`log_(2)`
`x^(9)` +
`log_(2)`
`y^(5)` -
`log_(2)` 8

= 9
`log_(2)` x + 5
`log_(2)` y -
`log_(2)` 8

The final expression using the properties of logarithm is 9
`log_(2)` x + 5
`log_(2)` y -
`log_(2)` 8.