1. **Problem:** Find the value of $x$ if $16^{245} = 32^x$. 2. **Formula and rules:** Express both sides with the same base. Note that $16 = 2^4$ and $32 = 2^5$. 3. **Rewrite the equation:** $$16^{245} = (2^4)^{245} = 2^{4 \times 245} = 2^{980}$$ $$32^x = (2^5)^x = 2^{5x}$$ 4. **Equate the exponents:** $$2^{980} = 2^{5x} \implies 980 = 5x$$ 5. **Solve for $x$:** $$x = \frac{980}{5} = \cancel{\frac{980}{5}} = 196$$ **Final answer:** $x = 196$