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Question 895141: 2^(x-1)+2^(x-1)=2860 find the value of x ? (Surds and indices)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 2^(x-1) + 2^(x-1) = 2*2^(x-1)
your formula becomes:
2*2^(x-1) = 2860
divide both sides by 2 to get:
2^(x-1) = 1430
take log of both sides to get:
log(2^(x-1) = log(1430
since log(2^(x-1)) = (x-1)*log(2), your equation becomes:
(x-1)*log(2) = log(1430)
divide both sides by log(2) to get:
x-1 = (1og(1430)/log(2)
add 1 to both sides to get:
x = log(1430)/log(2) + 1
solve for x to get x = 11.48179...
confirm by going back to the original equation to get:
2^(11.28179... - 1) + 2^(11.28179... - 1) = 2860
solve to get:
2860 = 2860.
your answer is that x = 11.48179943...
the value for x was internally stored in my calculator.
all calculations were done using the stored number.
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