Question

solve it with solution

Answer 1

Hey there !!


▶Solve :-

$\bf {5}^{ \sqrt{x} } \times {2}^{ \sqrt{y} } = 100.$

[ Now, can we right 100 = 25 × 4 , Because 25 × 4 = 100 . ]


$\bf {5}^{ \sqrt{x} } \times {2}^{ \sqrt{y} } = 100. \\ \\ = > \bf {5}^{ \sqrt{x} } \times {2}^{ \sqrt{y} } = 25 \times 4. \\ \\ \\ = > \bf { \cancel5}^{ \sqrt{x} } \times { \cancel2}^{ \sqrt{y} } = { \cancel5}^{2} \times { \cancel2}^{2} . \\ \\ = > \sqrt{x} \times \sqrt{y} = 2 \times 2. \\ \\ = > {x}^{ \frac{1}{2} } \times {y}^{ \frac{1}{2} } = 4. \\ \\ = > {x}^{ \frac{1}{2} } \times {y}^{ \frac{1}{2} } = \sqrt{4} \times \sqrt{4} . \\ \\ = > {x}^{ \cancel\frac{1}{2} } \times {y}^{ \cancel\frac{1}{2} } ={4}^{ \cancel\frac{1}{2} } \times {4}^{ \cancel\frac{1}{2} } . \\ \\ = > x \times y = 4 \times 4. \\ \\ \\ = > \therefore x = 4 \: and \: y = 4. \: ans \checkmark \checkmark$



▶ Verification :-

$\bf {5}^{ \sqrt{x} } \times {2}^{ \sqrt{y} } . \\ \\ = {5}^{ \sqrt{4} } \times {2}^{ \sqrt{4} } . \\ \\ = {5}^{2} \times {2}^{2} . \\ \\ = 25 \times 4. \\ \\ = 100.$

Hence, it is solved.


THANKS


#BeBrainly.

Answer 2

Giveen,

$5^{\sqrt{x}}\times2^{\sqrt{y}}=100\\\;\\\text{Making square of both sides}\\\;\\(5^{\sqrt{x}}\times2^{\sqrt{y}})^2=100^2\\\;\\5^{x}}\times2^{y}}=(25\times4)^2\\\;\\5^{x}}\times2^{y}}=(5^2\times2^2)^2\\\;\\5^{x}}\times2^{y}}=5^4\times2^4\\\;\\\text{On Camparing}\\\;\\x=4\\\;\\y=4\\\;\\\\\;\\Note:\\\;\\(a^m)^n=(a^n)^m=a^{mn}$