Question

please answer bhai bhai please​

Answer 1

Answer:

3

Explanation:

As per the provided information in the given question, we have :

$\longmapsto \rm {2^{-x} \times 2^{10} = 2^{3x} \times 2^{-2} }$

We are asked to calculate the value of x.

Basically, in this question, we have to use the laws of exponents.

$\longmapsto \rm {2^{-x} \times 2^{10} = 2^{3x} \times 2^{-2} }$

As we know that,

• $\bf a^m \times a^n = a^{m + n}$

So, applying this law, we can say that,

$\longmapsto \rm {2^{-x+10} = 2^{3x+(-2)} }$

Removing the brackets in the exponents of the number in R.H.S.

$\longmapsto \rm {2^{-x+10} = 2^{3x-2} }$

Since, the bases are same. So, the powers must be equal. Now, equating the powers,

$\longmapsto \rm { -x+10 = 3x-2 }$

Transposing like terms.

$\longmapsto \rm { 10 +2 = 3x +x}$

Performing addition in both L.H.S and R.H.S.

$\longmapsto \rm { 12 = 4x}$

Transposing 4 from R.H.S to L.H.S. Its arithmetic operator will get changed.

$\longmapsto \rm { \dfrac{12}{4} = x}$

Dividing 12 by 4.

$\longmapsto \bf { 3= x}$

∴ Value of x is 3.

$\rule{200}2$

Laws of exponents :

$\boxed{\begin{array}{cc}\bf{\dag}\:\:\underline{\bf{Law \; of \; Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{array}}$

Answer 2

Answer:-

$\\ \sf \longrightarrow \: {2}^{ - x} \times {2}^{10} = {2}^{3x} \times {2}^{ - 2} \\ \\ \sf \longrightarrow \: {2}^{ - x + 10} = {2}^{3x + ( - 2)} \\ \\ \sf \longrightarrow \: {2}^{ - x + 10} = {2}^{3x - 2} \\ \\ \sf \longrightarrow \: - x + 10 = 3x - 2 \\ \\ \sf \longrightarrow \: 3x + x = 10 + 2 \\ \\ \sf \longrightarrow \: 4x = 12 \\ \\ \sf \longrightarrow \: x = \frac{12}{4} \\ \\ \sf \longrightarrow \: x = 3$