Question

5. Find the value of m in the following:


please solve.
maths class 8​

Answer 1

a)

$\dfrac{ {2}^{m} }{ {2}^{ - 2} } = {2}^{3}$

${2}^{m - ( - 2)} = {2}^{3}$

${2}^{m + 2} = {2}^{3}$

$\implies m + 2 = 3$

$\boxed{m = 1}$

b)

$\dfrac{ {3}^{m} \times {3}^{6} }{ {3}^{ - 3} } = {3}^{18}$

${3}^{m + 6 - ( - 3)} = {3}^{18}$

${3}^{m + 9} = {3}^{18}$

$\implies m + 9 = 18$

$\boxed{m = 9}$

c)

$\dfrac{ {6}^{m} \times {6}^{3} \times {6}^{ - 2} }{ {6}^{ - 5} } = {6}^{12}$

${6}^{m + 3 - 2 - ( - 5)} = {6}^{12}$

${6}^{m + 3 - 2 + 5} = {6}^{12}$

${6}^{m + 6} = {6}^{12}$

$\implies m + 6 = 12$

$\boxed{m = 6}$