if 2^x+1=3^1-x then find the value of X
Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
2^(x+1)=3^(1-x)
take the log of both sides:
log[ 2^(x + 1) ] = log [ 3^(x - 1) ]
now use the property of logs => log(a^b) = b * log(a)
(x + 1) * log(2) = (x - 1) * log(3)
expand the (x + 1) and (x - 1) terms using distributive property => a*(b + c) = a*b + a*c
x * log(2) + 1 * log(2) = x * log(3) - 1 * log(3)
move all x terms to one side and all non-x terms to the other:
x * log(2) - x * log(3) = -1 * log(3) - 1 * log(2)
common factor the x:
x * [ log(2) - log(3) ] = -log(3) - log(2)
divide both sides by [ log(2) - log(3) ]:
x = [ -log(3) - log(2) ] / [ log(2) - log(3) ] = 4.41902