Question

2^m+n-4 x 3^n-m+6 = 6^2m+3n-5

Then find the value of m & n.

A. 5 and -1
B. 5 and -2
C. 4 and -2
D. 6 and -3
E. 6 and -2

Answer 1

Answer:

Option B

Step-by-step explanation:

Given,

       $2^{m+n-4}$ x $3^{n-m+6}$ = $6^{2m+3n-5}$

⇒    $2^{m+n-4}$ x $3^{n-m+6}$ = $($2 x 3)$)^{2m+3n-5}$

⇒    $2^{m+n-4}$ x $3^{n-m+6}$ = $2^{2m+3n-5}$ x $3^{2m-3n-5}$

By comparing both sides of equation,

$2^{m+n-4}=2^{2m+3n-5}$

⇒ m + n - 4 = 2m + 3n - 5

⇒ 2m + 3n - m - n = -4 + 5

⇒ m + 2n = 1

⇒ m = 1 - 2n ----------------------> ①

And,

$3^{n-m+6}=3^{2m+3n-5}$

⇒ n - m + 6 = 2m + 3n - 5

⇒ 2m + 3n - n + m = 6 + 5

⇒ 3m + 2n = 11

⇒ 3(1-2n) + 2n = 11

⇒ 3 - 6n + 2n = 11

⇒ -4n = 11 - 3

⇒ -n = 8/4

⇒ -n = 2

⇒ n = -2

m = 1 - 2n = 1 - 2(-2) = 1 + 4 = 5

∴ m = 5 and n = -2 (Option B)

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