Alg3.3.6

From Exampleproblems

Solve for $x$ : $3^{x+3}=9^{x+1}\,$

As a first step,we try to make the base equal as follows $3^{x+3}=(3^2)^{x+1}\,$

$3^{x+3}=3^{2x+2}\,$

Now since the two bases are equal,the two indices on both sides are equal to each other. $(x+3)=(2x+2)\,$

$x-2x=2-3\,$

$-x=-1\,$

Final solution is $x=1\,$