SOLUTION: Solve the exponential equation. 6^x-48*6^-x=2. What is the exact solution. What is the decimal approximation for the solution. Show all work.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the exponential equation. 6^x-48*6^-x=2. What is the exact solution. What is the decimal approximation for the solution. Show all work.      Log On


   

Question 639939: Solve the exponential equation. 6^x-48*6^-x=2. What is the exact solution. What is the decimal approximation for the solution. Show all work.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
6^x-48*6^-x=2
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6%5Ex+-+48%2A6%5E%28-x%29+=+2
Multiply by 6^x
6%5E%282x%29+-+48+=+2%2A6%5Ex
Sub y for 6^x
y%5E2+-+48+=+2y
y%5E2+-+2y+-+48+=+0
(y-8)*(y+6) = 0
y = -6 --> 6^x = -6 not allowed.
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y = 8 --> 6^x = 8
x*log(6) = log(8)
x = log(8)/log(6)
or x+=+log%286%2C8%29
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x =~ 1.160558
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After doing this, I see I could have made it simpler:
6%5Ex+-+48%2A6%5E%28-x%29+=+2
Sub y here
y - (48/y) = 2
etc