Question

answer is 3 please help​

Answer 1

Given:-

• $\dfrac{ {2}^{(2x - 2)} + 10}{13} = 2$

To find:-

• The value of x.

Answer:-

Given that,

$\dfrac{ {2}^{(2x - 2)} + 10}{13} = 2$

$\longrightarrow {2}^{(2x - 2)} + 10 = 2 \times 13$

$\longrightarrow {2}^{(2x - 2)} + 10 = 26$

$\longrightarrow {2}^{(2x - 2)} = 26 - 10$

$\longrightarrow {2}^{(2x - 2)} = 16$

We know that, 16 = 2⁴. So,

$\longrightarrow {2}^{(2x - 2)} = {2}^{4}$

As the bases are same (2), we can equate the exponents.

$\longrightarrow 2x - 2 = 4$

$\longrightarrow 2x = 4 + 2$

$\longrightarrow 2x = 6$

$\longrightarrow x = \dfrac{6}{2}$

$\longrightarrow x = 3$

Hence the value of x is,

$\longrightarrow \underline{ \underline{x = 3}}$