# solve 3^x+2=11

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Remember to first get your unknown on one side of the equation--in this case x. Since there are numbers on both sides, you can first subtract the "2" from both sides. So:

3^x + 2 = 11

becomes 3^x = 9

3 to what power equals 9 then becomes the question;

3^2 = 9, so x=2

The equation 3^x+2=11 has to be solved.

Subtract 2 from both sides of the equations.

3^x + 2 - 2 = 11 - 2

3^x = 9

Now express 9 as a power of 3, 9 = 3^2

3^x = 3^2

As the base is equal of both the sides of the equation, the exponent can be equated

This gives the solution of the equation x = 2

At x = 2, 3^x + 2 = 3^2 + 2 = 9 + 2 = 11

I tell my students to work these types of problems backwards. Start with the 11. Since 2 was added to the other side of the equation, to work backwards, subtract 2 from both sides first. 11 - 2 = 9. Now you have 3^x=9. So 3 to what power equals 9. My students can do this part in their heads. 3^2=9.

x = 2 because 3^2 = 9 and 9 + 2 = 11