The product of two rational numbers is rational.

The product of two rational numbers is always rational

Proof:

Let a = p/q and b = r/s be two rational numbers. We will have p,q,r,s be integers where denominators q and s are nonzero. We cannot divide by zero.

Multiplying a and b gives

a*b = (p/q)*(r/s) = (p*r)/(q*s)

Due to the closure property of integer multiplication, the expressions p*r and q*s are integers. The result we get is in the form of integer/integer. Basically we have two integers being divided. Furthermore, q*s is nonzero as neither q nor s is zero.

Therefore, if a and b are rational, then a*b is also rational as well.

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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