Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. assume that all variables represent positive real numbers. log base two of eight minus log base two of z. log base two of z divided by eight. log base two of eight divided by z. log base two of eight minus z. log base four of eight divided by z.

2log₂(x) +3log₂(y) -log₂(9)

Step-by-step explanation:

The applicable rules of logarithms are ...

... log(ab) = log(a) + log(b)

... log(a^b) = b·log(a)

... log(a/b) = log(a) -log(b)

Note that these are essentially all the same rule, expressed in different forms. For example, ...

... log(a·a) = log(a²) = log(a) +log(a) = 2·log(a)

The same sort of result obtains with larger exponents or exponents that are negative.

... log(a/b) = log(a·b⁻¹) = log(a) +(-1)log(b) = log(a) -log(b)

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Applying these to your problem, you have ...

... log₂(x²y³/9) = log₂(x²) +log₂(y³) -log₂(9)

... = 2log₂(x) +3log₂(y) -log₂(9)

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)