1. **State the problem:** Find the value of $x$ such that $\log_2 \left(\frac{1}{128}\right) = x$. 2. **Recall the logarithm definition:** $\log_b a = c$ means $b^c = a$. 3. **Rewrite the equation using the definition:** $2^x = \frac{1}{128}$. 4. **Express 128 as a power of 2:** $128 = 2^7$. 5. **Rewrite the right side:** $\frac{1}{128} = 2^{-7}$. 6. **Set the exponents equal:** Since $2^x = 2^{-7}$, then $x = -7$. **Final answer:** $x = -7$.