Question: 3^x-3^x-2=72

Posted by: Abraar I. on 08.10.2020

3^x-3^x-2=72 3^x-3^x/9 = 72 because 3^-2 =1/9 Multiplying by 9 9*3^x-3^x=72*9 8*3^x = 72*9 3^x = 9*9 =3^4 x = 4

3^x -3^x-2 = 72

3^x( 1- 1/9) = 72

3 ^x ( 8/9) = 72

3 ^ x = 81

3^ x = 3^4

x=4

Solution:

The given exp. can be written as :  3^x.(1 - 1/9) = 72 .  => 3^x.8/9 = 72    => 3^x = 81 = 3^4

Hence, x = 4 .   (Ans.)

Problem

Question: If 3^x -3^x-2 =72, then what is the value of x?

(How? See the solving 1-12 steps below)

Solving steps:

1: 3^x – (3^x * 3^-2) =72

[Since 3^x-2 can be written as 3^x * 3^-2]

2: 3^x – (3^x * 1/3^2) = 72

[Since 3^-2 can be written as 1/3^2]

3: 3^x – (3^x * 1/9) = 72 or 3^x – (3^x / 9) = 72

4: 3^x * (1 – 1/9) = 72

[Since 3^x is common, so take it out]

5: 3^x * [(9-1)/9] = 72

[By taking LCM]

6: 3^x * [8/9] = 72

7: 3^x = 72 * (9/8)

[By bringing 8/9 from LHS to RHS]

8: 3^x = 9 * 9

[By dividing 72 by 8]

9: 3^x = 3^2 * 3^2

(Since 9 can be written as 3*3 or 3^2)

10: 3^x = 3^(2+2)

(Since a^x * a^y = a^x+y)

11: 3^x = 3^4

12:  x = 4

(If base are same, then power values are also equal)

Note: * means multiplication. LHS means Left Hand Side. RHS means Right Hand Side

3^x  - 3^(x-2) =  72 .That is 3^(x-2){ 3^2-1}= 72

Therfore 3^(x-2)*(9-1) =72 or  3^(x-2)=  72/8= 9

Therfore 3^(x-2)= 9= 3^2 wich gives  x-2= 2  or  x=4

Ans:  x-4

X=4
X=4

Take 3^x common and simplify what remains in brackets, solve for x.

3^x (1 - 1/9) = 72,

3^x * 8/9 = 72,

3^x = 81 = 3^4,

x=4

4

x = 4,

Ans is 4
72 break in 81-9
3^x-3^x-2=72 3^x(1-3^-2)=72 3^x(1-1/9)=72 3^x(8/9)=72 3^x=72Ã—9/8 3^x=9Ã—9 3^x=3^4 comparing exponent x=4 Answer

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