Q. 4 - Precalculus Enhanced with Graphing Utilities

Question

In Problems $1-6$, solve each equation.

$3^x=9^{x+1}$.

Step-by-Step Solution

Answer

The solution for the equation $3^x=9^{x+1}$ is, $x=-2$.

Step 1 Given equation is,

$3^x=9^{x+1}$.

We know that, $3^2=9$.

So, the given equation becomes,

$3^x=3^{2(x+1)}$

Step 2 The expression obtained above can be solved since the radical of the exponentials on both the sides are same by equating the radicand of both the exponentials.

$x=2\left(x+1\right)$

Now simplify the obtained equation.

$$\begin{gathered} x=2x+2 \\ x-2x=2 \\ -x=2 \\ x=-2 \end{gathered}$$