Solve for x 3^(2x)+3^(x+1)-4=0

Problem

3(2*x)+3(x+1)−4=0

Solution

1. Rewrite the equation using exponent rules to isolate 3

3(2*x)+3⋅3−4=0

2. Substitute u=3 to transform the equation into a quadratic form.

u2+3*u−4=0

3. Factor the quadratic equation.

(u+4)*(u−1)=0

4. Solve for u by setting each factor to zero.

u=−4

u=1

5. Substitute back 3 for u and solve for x

3=−4

3=1

6. Evaluate the solutions. Since 3 must be positive for any real x 3=−4 has no real solution.

3=3

x=0

Final Answer

x=0

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