You are proving the Quotient Rule of Logarithms. The following shows your work so far.
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.
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 .
What value correctly evaluates log7492+log77 using the properties of logarithms?(1 point)
Responses
6
6
4
4
5
5
3
5.
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
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)