Question

How do I solve this?

Answer 1

Answer:

  x ≈ -4.419

Step-by-step explanation:

Separate the constants from the exponentials and write the two exponentials as one. (This puts x in one place.) Then use logarithms.

  0 = 2^(x-1) -3^(x+1)

  3^(x+1) = 2^(x-1) . . . . . add 3^(x+1)

  3×3^x = (1/2)2^x . . . . .factor out the constants

  (3/2)^x = (1/2)/3 . . . . . divide by 3×2^x

Take the log:

  x·log(3/2) = log(1/6)

  x = log(1/6)/log(3/2) . . . . . divide by the coefficient of x

  x ≈ -4.419

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A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.

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Comment on alternate solution

Once you get the exponential terms on opposite sides of the equal sign, you can take logs at that point, if you like. Then solve the resulting linear equation for x.

  (x+1)log(3) = (x-1)log(2)

  x=(log(2)+log(3))/(log(2)-log(3))