Solve the exponential equation without using logarithms.
$4^{- x} = 16^{x + 12}$
$x = ◻ (Simplify your answer.)$

Answer

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Answer

Final Answer: $x = - 8$

Steps

Step 1 ：Rewrite the equation with the same base: $(2^{2})^{- x} = (2^{4})^{x + 12}$

Step 2 ：Simplify the equation using the power of a power rule: $2^{- 2 x} = 2^{4 x + 48}$

Step 3 ：Set the exponents equal to each other since the bases are the same: $- 2 x = 4 x + 48$

Step 4 ：Solve for x: $x = - 8$

Step 5 ：Final Answer: $x = - 8$