Step-by-step explanation:
9. log(2)=a, log(3)=b, then log(36)=______
log(36) = log(6*6) = log(6) + log(6)
log(36)= log(6) + log(6)
log(36) = log(3*2) + log(3*2)
log(36) = (log(3) + log(2)) + (log(3) + log(2))
log(36) = (a + b) + (b + a)
log(36) = a + b + b + a
log(36) = 2a + 2b
<u><em>Answer:</em></u>
A box of 50 stickers would cost $13
<u><em>Explanation:</em></u>
<u>1- getting the equation representing the price:</u>
We have two variables; the number of stickers and the price of the box
We can note that the price is the dependent variable (y) while the number of stickers is the independent one (x)
<u>We are given that:</u>
A box of 15 stickers cost $6..........> first point is (15,6)
A box of 25 stickers cost $8 ........> second point is (25,8)
The general equation of the linear line is:
y = mx + c
where m is the slope and c is the y-intercept
<u>i. getting the slope:</u>
The equation now became: y = 0.2x + c
<u>ii. getting the y-intercept:</u>
To get the y-intercept, use any of the given points and substitute in the equation we got in part i. I will use the point (15,6)
y = 0.2x + c
6 = 0.2(15) + c
c = 6 - 0.2(15) = 3
<u>The final equation is:</u>
y = 0.2x + 3
where y is the price of the box and x is the number of stickers it contains
<u>2- getting the price of a box with 50 stickers:</u>
To get the price of a box of 50 stickers, simply substitute with x = 50 in the equation we got from part 1
<u>This is done as follows:</u>
y = 0.2(50) + 3 = 13
Therefore, a box of 50 stickers will cost $13
Hope this helps :)