Questions: Question 14 Solve the equation by relating the bases: 2^(x-3)=16 (A) x=5 (B) x=4 (C) x=7 (D) No solution

Transcript text: Question 14 Solve the equation by relating the bases: $2^{(x-3)}=16$ (A) $x=5$ (B) $x=4$ (C) $x=7$ (D) No solution Question 15

Solution

Step 1: Rewrite 16 as a power of 2

Since $16$ can be expressed as $2^4$, rewrite the equation as: \[ 2^{(x-3)} = 2^4 \]

Step 2: Set the exponents equal to each other

Since the bases are the same, set the exponents equal: \[ x - 3 = 4 \]

Step 3: Solve for $x$

Add $3$ to both sides of the equation to solve for $x$: \[ x = 4 + 3 \] \[ x = 7 \]

The correct answer is C. $ \boxed{x = 7} $

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