Question

Solve for x if 2(3^x-3^(x-1))=324

Answer 1

2(3^x-3^x-1)=324
3^x-3^(x-1)=162
3^(x-1)=3^4
x-1=4
x=5

Answer 2

Given,

• $2(3^x -3^{x-1}) = 324$ is given.

To find,

• Value of x

Solution,

The value of x for $2(3^x -3^{x-1}) = 324$ is 5.

We can simply find the value of x by using the laws of exponents.

                        $2(3^x -3^{x-1}) = 324$

                         $(3^x -3^{x-1}) = 324/2$

                         $(3^x -3^{x-1}) = 162$

162 can be written as (3)⁴* 2.

                       $(3^x -3^{x-1}) = 2 * 3^4$

Taking $3^{x-1}$ common, we get

                    $3^{x-1}$($3-1) = 24$  

                    $3^{x-1} * 2 = 2 * 3^4$

                            $3^{x-1}$$= 3^4$

Since the same bases have the same powers, equating the powers, we get

                           $x-1 = 4$

                                 $x = 4+1$

                                 $x=5$

Hence, the value of x for $2(3^x -3^{x-1}) = 324$ is 5.