SOLUTION: given the following three equations, solve for a, b, and c: 7^a * 7^b = 7^c (2^a)^b = 64 (3^b)/(3^c) = 1/9 thankz:D

Algebra ->  Finance -> SOLUTION: given the following three equations, solve for a, b, and c: 7^a * 7^b = 7^c (2^a)^b = 64 (3^b)/(3^c) = 1/9 thankz:D      Log On


   

Question 194947: given the following three equations, solve for a, b, and c:
7^a * 7^b = 7^c
(2^a)^b = 64
(3^b)/(3^c) = 1/9
thankz:D
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
given the following three equations, solve for a, b, and c:
7^a * 7^b = 7^c
(2^a)^b = 64
(3^b)/(3^c) = 1/9
:
Take each equation and simplify it:
:
7%5Ea+%2A+7%5Eb+=+7%5Ec
Add exponents when you multiply
7%5E%28a%2Bb%29+=+7%5Ec
therefore we can say:
a + b = c
:
%282%5Ea%29%5Eb+=+64
Multiply exponents when you raise it to another power
2%5E%28ab%29+=+64
64 is the 6th power of two
2%5E%28ab%29+=+2%5E6
therefore we can say:
ab = 6
:
%283%5Eb%29%2F%283%5Ec%29+=+1%2F9+
we subtract the dividing exponent, 9 is the 2nd power of three
3%5E%28b-c%29=+1%2F3%5E2+
which is
3%5E%28b-c%29+=+3%5E-2+
therefore we can say:
b - c = -2
:
Rearrange and solve using elimination method on the 1st and 3rd equations
a + b - c = 0
0 + b - c = -2
----------------subtraction eliminates b and c, find a
a = +2
:
Find b using: ab = 6
2b = 6
b = 6/2
b = 3
:
Find c using b - c = -2
3 - c = -2
-c = -2 - 3
-c = -5
therefore
c = +5
;
;
Try these three solutions in each original equation.