Question

In the following exercises, solve each equation.

$e^{3x}·e^4=e^{10}$

Short answer

The answer is$x=2$

Step-by-step solution

Step 1. Given

The equation is$e^{3x}·e^4=e^{10}$

Step 2. Solve the equation

$$\begin{gathered} e^{3x}·e^4=e^{10} \\ {e}^{3x+4}=e^{10} \end{gathered}$$

Bases are same so the exponents should be equal.

$$\begin{gathered} 3x+4=10 \\ 3x=10-4 \\ 3x=6 \\ x=2 \end{gathered}$$

Step 3. Check the answer

Put$x=2$in given equation,

$$\begin{gathered} e^{3x}·e^4=e^{10} \\ {e}^{3\left(2\right)}·e^4=e^{10} \\ {e}^6·e^4=e^{10} \\ {e}^{6+4}=e^{10} \\ {e}^{10}=e^{10} \end{gathered}$$

True