You are proving the Quotient Rule of Logarithms. The following shows your work so far.

Question

Let logbm=x and logbn=y .

logbm=x is equivalent to bx=m .

logbn=y is equivalent to by=n .

Which of the following options best describes the next step you should take in this proof?

(1 point)
Responses

Write the difference between m and n as m−n=bx−by.
Write the difference between m and n as m minus n equals b superscript x baseline minus b superscript y baseline .

Write the sum of m and n as m+n=bx+by.
Write the sum of m and n as m plus n equals b superscript x baseline plus b superscript y baseline .

Write the quotient of m and n as mn=bxby.
Write the quotient of m and n as Start Fraction m over n End Fraction equals Start Fraction b superscript x baseline over b superscript y baseline End Fraction .

Write the product of m and n as mn=bxby.

Answer 1

Write the product of m and n as mn=bx+by.

Answer 2

Which option best describes how to show that the Product Rule of Logarithms works for the base 4 expression log416+log44 ?(1 point)
Responses

Evaluate both log416 and log44 and show that their product is equal to the value of log464.
Evaluate both logarithm subscript 4 baseline 16 and logarithm subscript 4 baseline 4 and show that their product is equal to the value of logarithm subscript 4 baseline 64 .

Evaluate both log416 and log44 and show that their sum is equal to the value of log464.
Evaluate both logarithm subscript 4 baseline 16 and logarithm subscript 4 baseline 4 and show that their sum is equal to the value of logarithm subscript 4 baseline 64 .

Evaluate both log416 and log44 and show that their sum is equal to the value of log420.
Evaluate both logarithm subscript 4 baseline 16 and logarithm subscript 4 baseline 4 and show that their sum is equal to the value of logarithm subscript 4 baseline 20 .

Evaluate both log416 and log44 and show that their product is equal to the value of log420.
Evaluate both logarithm subscript 4 baseline 16 and logarithm subscript 4 baseline 4 and show that their product is equal to the value of logarithm subscript 4 baseline 20 .

Answer 3

Evaluate both logarithm subscript 4 baseline 16 and logarithm subscript 4 baseline 4 and show that their product is equal to the value of logarithm subscript 4 baseline 64 .

Answer 4

What value correctly evaluates log7492+log77 using the properties of logarithms?(1 point)
Responses

6
6

4
4

5
5

3

Answer 5

5.

Answer 6

Expand the logarithm log3(h9) .(1 point)
Responses

log3h2
Start Fraction logarithm subscript 3 baseline h over 2 End Fraction

(h−2)
left parenthesis h minus 2 right parenthesis

log3(h−3)
logarithm subscript 3 baseline left parenthesis h minus 3 right parenthesis

log3h−2

Answer 7

log3h2

Answer 8

Rewrite the expression log3z+log32+log34 as a single logarithm.(1 point)
Responses

log3(z+6)
logarithm subscript 3 baseline left parenthesis z plus 6 right parenthesis

log3(6z)
logarithm subscript 3 baseline left parenthesis 6 z right parenthesis

log3(24z)
logarithm subscript 3 baseline left parenthesis 24 z right parenthesis

log3(8z)

Answer 9

log3(24z)