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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.

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Answer:

Choice B.

Step-by-step 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.

olayemiolakunle65

Answer:

nine times log base two of x plus five times log base two of y minus log base two of eight i.e 9 [tex]log_{2}[/tex] x + 5 [tex]log_{2}[/tex] y - [tex]log_{2}[/tex] 8.

Step-by-step explanation:

The question can be expressed mathematically as thus:

                  [tex]log_{2}[/tex] [( [tex]x^{9}[/tex] × [tex]y^{5}[/tex] ) ÷ 8]

              = [tex]log_{2}[/tex] [tex]x^{9}[/tex]  +  [tex]log_{2}[/tex] [tex]y^{5}[/tex] - [tex]log_{2}[/tex] 8

              =  9 [tex]log_{2}[/tex] x + 5 [tex]log_{2}[/tex] y - [tex]log_{2}[/tex] 8

The final expression using the properties of logarithm is 9 [tex]log_{2}[/tex] x + 5 [tex]log_{2}[/tex] y - [tex]log_{2}[/tex] 8.

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