If 2 10 + 2 10 = 2 x 2 10 + 2 10 = 2 𝑥 , what's x 𝑥 ?

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Full math Solution Here 

Given the equation:

$2^{10}+2^{10}=2^{𝑥}$

We start by recognizing the left-hand side:

$2^{10}+2^{10}$

We can factor out $2^{10}$ from both terms:

$2^{10}+2^{10}=2^{10}(1+1)$

Since $1+1=2$, we have:

$2^{10}(1+1)=2^{10}\cdot 2$

We can rewrite $2$ as $2^1$:

$2^{10}\cdot 2=2^{10}\cdot 2^1$

Using the property of exponents that ${𝑎}^{𝑚}\cdot {𝑎}^{𝑛}={𝑎}^{𝑚+𝑛}$, we get:

$2^{10}\cdot 2^1=2^{10+1}$

So,

$2^{11}=2^{𝑥}$

By comparing the exponents, we find:

$𝑥=11$

Thus, the value of $𝑥$ is $\boxed{{\displaystyle 11}}$.