SOLUTION: If 12 = r^y then what is the value of 12r ?

Question 624416: If 12 = r^y then what is the value of 12r ?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
12 = r^y
what is the value of 12r?
what you are doing is multiplying both sides of this equation by r to get:
12r = r^y*r
by the laws of exponents
x^a*x^b = x^(a+b)
since:
12r = r^y*r is the same as:
12r = r^y*r^1, then this becomes:
12r = r^(y+1)
an example will show this to be true.
we start with:
12 = r^y
we'll take a value of r at random.
let's assume that r = 3
our equation becomes:
12 = 3^y
we can use logs to solve this to get:
y = 2.261859507
you can use your calculator to confirm that:
12 = 3^(2.261859507)
we now multiply both sides of this equation by 3 to get:
3*12 = 3*3^(2.261859507)
using the rule above that states that:
12r = r^(y+1), we get:
3*12 = 3^(3.261859507)
using our calculator again, we get:
36 = 36, confirming the rule.
an easier example to understand would be as follows:
suppose the problem were:
100 = 10^2
y = 2 in this case.
r = 10
100 = 10^2 is the same as:
100 = r^y because r = 10 and y = 2
we now multiply both sides of this equation by r which means we multiply both sides of this equation by 10
we get:
100*10 = 10*10^2 which is the same as:
1000 = 10^1*10^2 which is the same as:
1000 = 10^(1+2) which is the same as:
1000 = 10^3 which is the same as:
1000 = 1000
this confirms the rule.
summary of all of this is that:
12 = r^y becomes:
12r = r(y+1) when you multiply both sides of that equation by r.

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