Jeff is baking a cake. The recipe says that he has to mix 32 grams of vanilla powder to the flour. Jeff knows that 1cup of the vanilla powder has the mass of 128 grams. He added 2/3 of a cup of vanilla powder to the flour. Should Jeff add more vanilla powder to make the exact recipe, or did he go over and by what amount?

Jeff added 52 grams more

Step-by-step explanation:

How much is 2/3 cup:

Jeff added 84 grams instead of 32 grams, so he added:

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