Solve for x 3^(2x)+3^x-30=0

Problem

3(2*x)+3−30=0

Solution

1. Rewrite the first term using the power of a power rule to make the equation look like a quadratic.

(3)2+3−30=0

2. Substitute a new variable u for 3 to simplify the equation.

u=3

u2+u−30=0

3. Factor the quadratic equation by finding two numbers that multiply to −30 and add to 1

(u+6)*(u−5)=0

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

u=−6

u=5

5. Back-substitute 3 for u and solve for x

3=−6

3=5

6. Evaluate the results. Since 3 must always be positive for real x the equation 3=−6 has no real solution.

3=5

7. Apply logarithms to solve for x in the remaining equation.

ln(3)=ln(5)

x*ln(3)=ln(5)

x=ln(5)/ln(3)

Final Answer

x=ln(5)/ln(3)

Want more problems? Check here!