Solve-2-x-3-y-72-i-2-y-3-x-108-ii-

Question Number 92013 by I want to learn more last updated on 04/May/20

Solve :

2^{x} + 3^{y} = 72 \dots . . (i)

2^{y} + 3^{x} = 108 \dots . . (ii)

Commented by jagoll last updated on 04/May/20

108 \times 2 = 216

why 416 ? ?

Commented by jagoll last updated on 04/May/20

x = y + 2

2^{y + 2} + 3^{y} = 72

2^{y} + 3^{y + 2} = 108

let 2^{y} = t \land 3^{y} = w

4 t + w = 72

t + 9 w = 108

now easy to solve

Commented by I want to learn more last updated on 04/May/20

Thanks sir, i appreciate .

Commented by I want to learn more last updated on 04/May/20

Why do we let x = y + 2

can i still say x = y + 5

Commented by jagoll last updated on 04/May/20

eq (1) \times by 3

eq (2) \times by 2

substract (1) & (2)

Commented by I want to learn more last updated on 04/May/20

3 (2^{x}) + 3^{y + 1} = 216

2^{y + 1} + 2 (3^{x}) = 216

Please next step here

2^{y + 1} - 3 (2^{x}) + 2 (3^{x}) - 3^{y + 1} = 0

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

Commented by I want to learn more last updated on 04/May/20

sir, show the steps till when you say let x = y + 2 .

i will do the rest

Commented by I want to learn more last updated on 04/May/20

Have changed it . please next steps .

Commented by I want to learn more last updated on 04/May/20

t = 15.429 and w = 10.286

2^{y} = 15.429

y = \frac{\ln (15.429)}{\ln (2)} = \frac{2.736}{0.6931} = 3.9475

x = 3.9475 + 2 = 5.9475

But not correct with the question

Commented by MJS last updated on 05/May/20

x = y + 2 is wrong

the path given to get x = y + 2 is wrong

Answered by MJS last updated on 04/May/20

approximating leads to

x \approx 4.15063

y \approx 3.63495

Commented by I want to learn more last updated on 04/May/20

But using the approach above, am not getting it