Question

In the following exercises,graph each of the following functions.

$3^{5x-6}=81$

Short answer

The solution is$x=2$.

Step-by-step solution

Step 1.Given information

Consider the given quadratic equation $3^{5x-6}=81$

Solve the equation for x as follows;

Step 2.First write both sides of the equation with the same base

Because left side of the equation has base 2,so write the right side of the equation with base 3 as

$$\begin{gathered} 3^{5x-6}=81 \\ {3}^{5x-6}=3^4[3^4=81] \end{gathered}$$

Because the base are same 3,so the exponent must be equal.

$5x-6=4$

Step 3.Now solve the equation

$$\begin{gathered} 5x-6+6=4+6[add6] \\ 5x=10 \\ \frac{5x}{5}=\frac{10}{5}[Divideby5] \\ x=2 \\ So,thevalueisx=2 \end{gathered}$$

Step 4.Check

To check the solution,replace x by 2 in original equation.

$$\begin{gathered} 3^{5.2-6}=81 \\ {3}^{10-6}=81 \\ {3}^4=81 \\ 81=81\left[true\right] \\ Therefore,thesolutionisx=2 \end{gathered}$$