Alg3.3.5

From Exampleproblems

Solve for $x$ : $2^{x+3}=4^{x+1}\,$

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

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

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

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

$-x=-1\,$

Final solution is $x=1\,$