Solve for x 5(1.2)^(3x-2)+1=7

Problem

5*(1.2)^(3*x−2)+1=7

Solution

1. Isolate the exponential term by subtracting 1 from both sides of the equation.

5*(1.2)^(3*x−2)=6

2. Divide both sides by 5 to further isolate the base and exponent.

(1.2)^(3*x−2)=1.2

3. Identify that the right side of the equation can be written with an implicit exponent of 1.

(1.2)^(3*x−2)=(1.2)^1

4. Equate the exponents since the bases on both sides are identical.

3*x−2=1

5. Solve the resulting linear equation for x by adding 2 to both sides.

3*x=3

6. Divide by 3 to find the final value of x

x=1

Final Answer

x=1

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