Powers and Roots – Solving exponential equation – Exercise 5577

Exercise

Solve the equation:

{(\sqrt{3})}^{3-x}=9^{x+2}

Final Answer

Show final answer

Solution

Using Powers and Roots rules we get:

{(\sqrt{3})}^{3-x}=9^{x+2}

3^{\frac{1}{2}(3-x)}=3^{2(x+2)}

\frac{1}{2}(3-x)=2(x+2)

3-x=4(x+2)

3-x=4x+8

-5x=5

x=-1