Question

If 2^x+1 = 3^1-x then find value of x.

Answer 1

2^(x +1) = 3^(x - 1) 

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 

Answer 2

Answer:

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