Question

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.
7log x + 2log y

log(14xy)

log(x7 + y2)

log(x7y2)

log(7x + 2y)

Answer 1

Answer:

log(x^7·y^2)

Step-by-step explanation:

The applicable rules are ...

... log(a^b) = b·log(a)

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

_____

The first term, 7log(x) can be rewritten as log(x^7). Note that an exponentiation operator is needed when this is written as text.

The second term 2log(y) can be rewritten as log(y^2). These two rewrites make use of the first rule above.

Now, you have the sum ...

... log(x^7) +log(y^2)

The second rule tells you this can be rewritten as ...

... log(x^7·y^2) . . . . . seems to match the intent of the 3rd selection