Solve the equation. \( 3^{x-5}=243 \) \( x=[?] \)

To solve the equation: \[ 3^{x-5} = 243 \] **Step 1: Express 243 as a Power of 3** First, recognize that \( 243 \) can be written as a power of \( 3 \): \[ 243 = 3^5 \] **Step 2: Rewrite the Original Equation** Substitute \( 243 \) with \( 3^5 \) in the original equation: \[ 3^{x-5} = 3^5 \] **Step 3: Set the Exponents Equal** Since the bases are the same and the equation holds true, the exponents must be equal: \[ x - 5 = 5 \] **Step 4: Solve for \( x \)** Add \( 5 \) to both sides of the equation to isolate \( x \): \[ x = 5 + 5 \] \[ x = 10 \] **Final Answer:** \[ x = 10 \]