Solve the equation 9 = square root of 27(4x + 6). Using complete sentences, explain the strategy used in solving this equation.

Question

Solve the equation 9 = square root of 27^(4x + 6). Using complete sentences, explain the strategy used in solving this equation.

Answer 1

The square root of a number is the same as raising that number to the ½ power.

 

So , we have 9 = (27^{4x + 6})^½.

 

Multiply the exponents to get 9 = 27^{2x + 3}.

 

Since 9 and 27 are both powers of 3, we can rewrite the equation in the form  3² = (3³)^{2x + 3}

 

Multiply the exponents on the right side of the equation                     to get 3² = 3^{6x + 9}.

 

So, 2 = 6x + 9.  

     -7  = 6x

 

x = -7/6