Question

Question is 5 raised to the power of -4x multiplied by 5 raised to the power of x square+ 4 is equal to = 1.
Then find the value of x.
Correct answer will be marked as brainliest . And please don't spam.​

Answer 1

Answer:

$\large{\boxed{\boxed{\sf{Question}}}}$

$\bf \:Solve \: for \: x :- {5}^{ - 4x} \times {5}^{ {x}^{2} + 4} = 1$

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

$\bf \: {5}^{ - 4x} \times {5}^{ {x}^{2} + 4} = 1$

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Value of x

Identity used :-

$\bf \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

$\bf \: {a}^{0} = 1$

$\bf \: {a}^{m} = {a}^{n} ⟹ \: m = n$

$\large{\boxed{\boxed{\sf{Solution}}}}$

$\bf \: {5}^{ - 4x} \times {5}^{ {x}^{2} + 4} = 1$

$\bf\implies \: {5}^{ - 4x \: + \: {x}^{2} + 4} = {5}^{0}$

$\bf\implies \: {x}^{2} - 4x + 4 = 0$

$\bf\implies \: {x}^{2} - 2x - 2x + 4 = 0$

$\bf\implies \:x(x - 2) - 2(x - 2) = 0$

$\bf\implies \:(x - 2)(x - 2) = 0$

$\bf\implies \:x = 2$

_____________________________________________