Question

2^x * 2^10 = 2^-4x find x

Answer 1

-2

Explanation:

Given:

${2}^{x} . {2}^{10} = {2}^{ - 4x}$

To Find:

The value of x

Solution:

${2}^{x}. {2}^{10} = {2}^{-4x} \\ \\ {2}^{x + 10} = {2}^{-4x}$

[Eliminating Base from both sides]

$x + 10 = - 4x \\ \\ x + 4x = - 10 \\ \\ 5x = - 10 \\ \\ \cancel{5}x = - \cancel{10} \\ \\ x = - 2$

Therefore the required answer is -2.

${\boxed{\red{\textsf{Some Important Laws of Indices}}}}$

${a}^{n}.{a}^{m}={a}^{(n + m)}$

${a}^{-1}=\dfrac{1}{a}$

$\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}$

${({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}$

${a}^{\frac{1}{x}}=\sqrt[x]{a} \\\\ a^0 = 1$

[Where all variables are real and greater than 0]