Powers and Roots – Solving exponential equation – Exercise 5577

Exercise

Solve the equation:

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

Final Answer


x=1x=-1

Solution

Using Powers and Roots rules we get:

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

312(3x)=32(x+2)3^{\frac{1}{2}(3-x)}=3^{2(x+2)}

12(3x)=2(x+2)\frac{1}{2}(3-x)=2(x+2)

3x=4(x+2)3-x=4(x+2)

3x=4x+83-x=4x+8

5x=5-5x=5

x=1x=-1

Share with Friends

Leave a Reply