Solve for x 2^(x-3)=16

Problem

2(x−3)=16

Solution

1. Rewrite the right side of the equation as a power of 2 to match the base on the left side.

16=2

2. Substitute the new expression back into the original equation.

2(x−3)=2

3. Apply the property of equality for exponential functions, which states that if by=bz then y=z

x−3=4

4. Solve for x by adding 3 to both sides of the equation.

x=4+3

x=7

Final Answer

x=7

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