Ava went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 40 grams of sugar and each bottle of juice has 20 grams of sugar. Ava purchased a total of 11 bottles of juice and soda which collectively contain 400 grams of sugar. Graphically solve a system of equations in order to determine the number of bottles of soda purchased, x, x, and the number of bottles of juice purchased, yy.

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x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752