Question

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

Answer 1

Answer:

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

Hope it helps!

Answer 2

Answer:

2^x+1=3^1−x

taking log both side

(x+1log2=(1−x)log3

x=

log1+log3

log3−log2

hope it will helps you

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