Question

Solve the equation 9 = square root of 3(4x + 6). Using complete sentences, explain the strategy used in solving this equation

Answer 1

\[9=\sqrt{3^{4x+6}}\]

Answer 2

Write the left side as a power of 3.
Write the right side as a power of 3.
If two powers of 3 are equal, then the exponents must be equal.

Example:
\( \large{\sqrt{3^p} = (\sqrt{3})^p = (3^{\frac{1}2})^p = 3^{\frac{1}{2}p} }\)

Answer 3

so \[3^{2}=3^{\frac{ 1 }{ 2 }(4x=6)}\]?