Question

please tell me the ANSWER ​

Answer 1

GIVEN :

${3}^{m} = 9 \times {3}^{n}$

$8 \times {2}^{n} = {4}^{m}$

To find :

the value of m and n

CONCEPT USED :

${a}^{g} \times {a}^{h} = {a}^{g + h}$

SOLUTION :

$= > {3}^{m} = 9 \times {3}^{n}$

$= > {3}^{m} = {3}^{2} \times {3}^{n}$

using the concept :-

${a}^{g} \times {a}^{h} = {a}^{g + h}$

$= > {(3)}^{m} = {(3)}^{2 + n}$

therefore , m = 2+n......(1)

$= > 8 \times {2}^{n} = {4}^{m}$

$= > { (2)}^{3} \times {2}^{n} = {4}^{m}$

$= > { (2)}^{3 + n} = {2}^{2m}$

3 + n = 2m

(3+n) /2=m......(2)

from (1) and (2) :-

=> (3 + n) /2= 2+n

now ,cross multiply :-

=> (3 + n) = (2+n)×2

=> (3 + n) = 4+2n

=> 3 -4 = 2n-n

=> 3 -4 = 2n-n

=> -1 = n

put n= -1 in m = 2+n to get the value of m.

=> m = 2+n

=> m = 2-1

=> m = 1

ANSWER :

n = -1

m = 1