If, 3^(2x+y)=243 and 2^(x+2y)=256, then 6x+3y = ?

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13 Jul 2022 Algebra

If, 3^(2x+y)=243 and 2^(x+2y)=256, then 6x+3y = ?

OPtion

1) 13/3
2) 11/3
3) 2/3
4) 12
5) 15
6) 18
7) 24
8) 30
9) 27
10) None of these

Solution

Given, 3^(2x+y)=243
⇒ 3^(2x+y) = 3^5
Comparing powers of a equal base: 2x+y = 5 ---(i)
Similarly, 2^(x+2y)=256
⇒ 2^(x+2y) = 2^8
x+2y = 8 ---(ii)
Solving, eqn. (i) & (ii), we get, x=2/3, y=11/3
.'. 6x+3y = 6*(2/3) + 3*(11/3) = 15
Correct Option 5)

Correct Option: 5 Best Solution (2)

G.S.Kantharao   1 year AGO

=3^(2x+y)=3^5 and 2^(x+2y)=2^8
2x+y=5....i
x+2y=8....ii
now ii - i
4x+2y=10
x +2y=8=>x=2/3
And I + ii
3x+3y=13
so X =2/3 and Y =11/3
now 6x+3y=3x+3x+3y=3*2/3+13
=15
so My option is 5 👈
Another Simple method
Given 3^(2x+y)=243=3^5
{3^(2x+y)}^3=(3^5)^3
6x+3y=15
My option is 5 👈

Like? Yes (2) | No   

Dr.Dipin Singh   1 year AGO

3^(2x+y) =243=3^5
2x+y=5
6x+3y=15

Like? Yes (1) | No