Question

3^x-3^(x-1)=18 then the value of x.

Answer 1

Answer:

Required numeric value of x is 3.

Step-by-step explanation:

It is given that the value of 3^x - 3( x - 1 ) is 18

This problem can be solved by using two methods.

  Method 1 for the solution

$\implies 3^x - \dfrac{3^x}{3^1}=18$

$\implies 3^x - \dfrac{3^x}{3}=18$

$\implies 3^x \bigg\{1 - \dfrac{1}{3}\bigg\}=18$

$\implies 3^x \bigg\{ \dfrac{3-1}{3}\bigg\}=18$

$\implies 3^x \times \dfrac{2}{3}=18$

$\implies 3^x =18\times \dfrac{3}{2}$

$\implies 3^x =27$

$\implies 3^x = 3^3$

Comparing values, we get : -

x = 3

     Method 2 for the solution

$\implies 3^x - 3^{x-1}=18$

$\implies 3^x - 3^{x-1}=27-9$

$\implies 3^x - 3^{x-1}=3^3 - 3^{2}$

$\implies 3^x - 3^{x-1}=3^3 - 3^{3-1}$

Comparing both sides,

x = 3

Therefore the value of x is 3.