Chapter 4, Problem 64RE

To determine

To Find: The solution of the equation.

  $3^{2x}-3^x-6=0$

Answer to Problem 64RE

  $x=1$

Explanation of Solution

Given:Solve the equation. Find the exact solution of the equation if possible,otherwise use a calculator to approximate to two decimals.

  $3^{2x}-3^x-6=0$

Given: $3^{2x}-3^x-6=0$

Reducing it to form a quadratic polynomial

  ${(3^x)}^2-3^x-6=0$

Factoring the quadratic polynomial we get

  $(3^x-3)(3^x+2)=0$

Since, $(3^x+2)>0$ we can divide by it

  $\begin{array}{l}{3}^x=3=3^1\\ x=1\end{array}$

Hence, the solution of the equation is $x=1$