Could you help me in my homework??? (exponential equation)?

Question

solve for x:

2 ^2/3(x+1) = 3 x 2 ^1/3x + 20

tnx for the help..

Answer 1

It is not good to use "x" as multiplication when the equation contains "x" as the variable.  Either use parentheses or *.

Also, you need to use more parentheses.

I'll assume you mean

2^[2/3x+1] = 3(2^(1/3x)) + 20

We can rewrite 2^[2/3(x+1)] = 2^(2/3x) *2^1 = 2(2^(2/3x))

Then you have

2(2^(2/3x)) = 3(2^(1/3x)) + 20

Let y = 2^(1/3x), then y² = 2^(2/3x), so now we have

2y² = 3y + 20

Move everything to one side.

2y² - 3y - 20 = 0

(y-4)(2y+5) = 0

y = 4 or y = -5/2

Remember that y = 2^(1/3x).

So 2^(1/3x) = 4 or 2^(1/3x) = -5/2

The first one gives x = 6 as a solution, and the second one has no solution.

Answer: x = 6