Solve for x 3^(2x-7) = square root of 81^x

Problem

3(2*x−7)=√(,81)

Solution

1. Rewrite the square root using a fractional exponent.

3(2*x−7)=(81)1/2

2. Express the base 81 as a power of 3 to create a common base.

81=3

3. Substitute the new base into the equation.

3(2*x−7)=((3)x)1/2

4. Simplify the exponents on the right side by multiplying them.

3(2*x−7)=3(4⋅x⋅1/2)

3(2*x−7)=3(2*x)

5. Equate the exponents since the bases are now identical.

2*x−7=2*x

6. Solve for x by subtracting 2*x from both sides.

−7=0

7. Conclude that since the resulting statement is a contradiction, there is no value of x that satisfies the equation.

Final Answer

3(2*x−7)=√(,81)⇒No solution

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