SOLUTION: Use the properties of exponential and logarithmic functions to solve each system. {{{system(-2^(10-x)+y = 0, y = 8^(x+2))}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Use the properties of exponential and logarithmic functions to solve each system. {{{system(-2^(10-x)+y = 0, y = 8^(x+2))}}}       Log On


   

Question 1070040: Use the properties of exponential and logarithmic functions to solve each
system.
system%28-2%5E%2810-x%29%2By+=+0%2C+y+=+8%5E%28x%2B2%29%29

Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
 
system%28-2%5E%2810-x%29%2By+=+0%2C+y+=+8%5E%28x%2B2%29%29

The second equation is solved for y, so substitute
8x+2 for y in the first equation:

-2%5E%2810-x%29%2B8%5E%28x%2B2%29=0

Add 210-x to both sides:

8%5E%28x%2B2%29=2%5E%2810-x%29

Write 8 as 23

%282%5E3%29%5E%28x%2B2%29=2%5E%2810-x%29

Remove the parentheses on the left by multiplying the
exponents:

2%5E%283x%2B6%29=2%5E%2810-x%29

Now we use the principle that 
if BP = BQ, then P = Q

3x%2B6=10-x
4x=4
x=1

Substitute in 

y+=+8%5E%28x%2B2%29
y+=+8%5E%281%2B2%29
y+=+8%5E3
y=512

Answer: (x,y) = (1,512)

Edwin