Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variab
les 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.
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.
1 answer:
Answer:
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)
_____
Applying these to your problem, you have ...
... log₂(x²y³/9) = log₂(x²) +log₂(y³) -log₂(9)
... = 2log₂(x) +3log₂(y) -log₂(9)
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