Question

If
${16}^{2} \times {8}^{4} = {4}^{x}$
Find x

​

Answer 1

=

$= { {4}^{2} }^{2} \times {4}^{6} = {4}^{x}$

${4}^{4} \times {4}^{6} = {4}^{x}$

${4}^{10} = {4}^{x}$

$since \: bases \: are \: equal \: exponents \: must \: also \: be \: equal$

$x = 10$

Answer 2

${16}^{2} \times {8}^{4} = {4}^{x}$

$=> {2}^{8} \times {2}^{12} = {4}^{x}$

${(2)}^{8 + 12} = {4}^{x}$

${2}^{20} = {4}^{x} = {2}^{2x}$

base is same both sides now , so taking powers only we get-

$20 = 2x \\ x = \frac{20}{2} \\ x = 10$

Hence , x = 10