Find the greatest common factor of the following terms 10r^3 and -100r^4

For this case we have that by definition, the GCF of two expressions, is given by the greatest factor that divides both numbers, having an exact division.

We look for the factors of 10 and 100:

10: 1,2,5,10

100: 1,2,4,5,10,20,50,100

The biggest factor that divides both numbers is 10.

Now, is the greatest common factor of both expressions:

Then, is the greatest common factor of the expressions given:

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