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Given 2^{x + 1} = 4^{x - 3}Solve for x,

=> 2^{x + 1} = 4^{x - 3}=> 2^{x + 1} = (2^{2})^{x - 3}^{}^{} [(x^{m})^{n} = x^{mn} ]

=> 2^{x + 1} = 2^{2(x - 3)} ^{}

=> 2^{x + 1} = 2^{2x - 6}

[ If x^{m} = x^{n} then m = n ]

=> x + 1 = 2x - 6

=> 2x - x = 1 + 6

=> x = 7.**answer**

=> 2

=> 2

=> 2

[ If x

=> x + 1 = 2x - 6

=> 2x - x = 1 + 6

=> x = 7.

Let the present age of Samara = x years

and present age of Sasna = y years

**Step 1:**

Given:

The ages of Samara and Sasna are in the ratio 9 : 4

=> $\frac{x}{y} = \frac{9}{4}$

=> 4x = 9y

=> 4x - 9y = 0 ..............................(1)

**Step 2: **

**Seven years hence**

Age of Samara = x + 7 years

and the age of Sasna = y + 7 years

Ratio of Samara and Sasna's ages will be 5 : 3.

=> $\frac{x + 7}{y + 7} = \frac{5}{3}$

=> 3(x + 7) = 5(y + 7)

=> 3x + 21 = 5y + 35

=> 3x - 5y = 35 - 21

=> 3x - 5y = 14 ................................(2)

**Step 3:**

Multiply equation (1) by 3

=> 3(4x - 9y = 0)

=> 12x - 27y = 0 ................................(3)

Multiply equation (2) by 4

=> 4(3x - 5y = 14)

=> 12x - 20y = 56 ................................(4)

**Step 4:**

Solve equation (3) and equation (4)

Coefficient of 'x' is same in both the equations.

Subtract equation (3) from equation (4)

12x - 20y = 56

- 12x - 27y = 0

- + -

------------------------

0 + 7y = 56

-------------------------

=> 7y = 56

Divide each side by 7, to isolate y.

=> $\frac{7y}{7} = \frac{56}{7}$

=>** y = 8**, Sasna's age

**Step 5: **

Substitute y = 8 in equation (1)

=> 4x - 9 * 8 = 0

=> 4x - 72 = 0

Add 72 both sides

=> 4x - 72 + 72 = 72

=> 4x = 72

Divide each side by 4

=> $\frac{4x}{4} = \frac{72}{4}$

=>**x = 18**, Samara's age

**Answer:** Samara's age = 18 years

and Sasna's age = 8 years.

and present age of Sasna = y years

Given:

=> $\frac{x}{y} = \frac{9}{4}$

=> 4x = 9y

=> 4x - 9y = 0 ..............................(1)

Age of Samara = x + 7 years

and the age of Sasna = y + 7 years

Ratio of Samara and Sasna's ages will be 5 : 3.

=> $\frac{x + 7}{y + 7} = \frac{5}{3}$

=> 3(x + 7) = 5(y + 7)

=> 3x + 21 = 5y + 35

=> 3x - 5y = 35 - 21

=> 3x - 5y = 14 ................................(2)

Multiply equation (1) by 3

=> 3(4x - 9y = 0)

=> 12x - 27y = 0 ................................(3)

Multiply equation (2) by 4

=> 4(3x - 5y = 14)

=> 12x - 20y = 56 ................................(4)

Coefficient of 'x' is same in both the equations.

Subtract equation (3) from equation (4)

12x - 20y = 56

- 12x - 27y = 0

- + -

------------------------

0 + 7y = 56

-------------------------

=> 7y = 56

Divide each side by 7, to isolate y.

=> $\frac{7y}{7} = \frac{56}{7}$

=>

Substitute y = 8 in equation (1)

=> 4x - 9 * 8 = 0

=> 4x - 72 = 0

Add 72 both sides

=> 4x - 72 + 72 = 72

=> 4x = 72

Divide each side by 4

=> $\frac{4x}{4} = \frac{72}{4}$

=>

and Sasna's age = 8 years.