c) \( 8^{x-3}=4^{x-9} \)

To solve the equation \( 8^{x-3}=4^{x-9} \), we can start by expressing both sides with a common base. We know that \( 8 = 2^3 \) and \( 4 = 2^2 \). Thus, we can rewrite the equation in terms of base 2: \[ (2^3)^{x-3} = (2^2)^{x-9} \] This simplifies to: \[ 2^{3(x-3)} = 2^{2(x-9)} \] Now, since the bases are the same, we can set the exponents equal to each other: \[ 3(x-3) = 2(x-9) \] Expanding both sides gives us: \[ 3x - 9 = 2x - 18 \] Now, let’s isolate \( x \): \[ 3x - 2x = -18 + 9 \] This simplifies to: \[ x = -9 \] Thus, the solution to the equation \( 8^{x-3}=4^{x-9} \) is \( x = -9 \).