SOLUTION: Two problems evaluate the expression: http://i.imgur.com/3jdAZlF.png and Find the solution of the exponential equation, rounded to four decimal places. 10^(1 − x) = 2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Two problems evaluate the expression: http://i.imgur.com/3jdAZlF.png and Find the solution of the exponential equation, rounded to four decimal places. 10^(1 − x) = 2      Log On


   

Question 916725: Two problems
evaluate the expression:
http://i.imgur.com/3jdAZlF.png
and
Find the solution of the exponential equation, rounded to four decimal places.
10^(1 − x) = 2x
Please explain,
Thank you
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
10%5E%281-x%29=2x

log%2810%2C%2810%5E%281-x%29%29%29=log%2810%2C2x%29

log%2810%2C%2810%5E1%29%2F%2810%5Ex%29%29=log%2810%2C2x%29

log%2810%2C10%5E1%29-log%2810%2C10%5Ex%29=log%2810%2C2x%29

log%2810%2C10%5E1%29=log%2810%2C2x%29%2Blog%2810%2C10%5Ex%29

1=log%2810%2C%28%282x%29%2810%5Ex%29%29%29

1=log%2810%2C%282x%2A10%5Ex%29%29

10%5E1=2x%2A10%5Ex

2x%2A10%5Ex=10

x%2A10%5Ex=5

No way to completely find one formula for x. Numeric computation to approximately match the left and right sides may be the only way