Question

solve algebraically for x: 27^x=9^x+2

Answer 1

we can rewrite this equation to
(3^3)^x=(3^2)^x + 2

Answer 2

\[\left( 3^{3} \right)^{x}=\left( 3^{2} \right)x+2\]
\[3^{3x}=3^{2x}+2\]
\[\left( 3^{x} \right)^{3}=\left( 3^{x} \right)^{2}+2\]
substitute \[3^{x}=y\]
\[y ^{3}=y ^{2}+2\]
\[y ^{3}-y ^{2}-2=0\]
now you can solve for y and then for x