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Calculus IChapter 1: ReviewSection 1-9

Exponential and Logarithm Equations — Question 10

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Question 10

Solve the equation: 2x+1+2x=482^{x+1} + 2^{x} = 48

Instructions: Solve the equation algebraically. Express your answer in exact form and give an approximation rounded to three decimal places.

Original worksheet page 1: question and worked solution for 1-9-010
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Question 10 - Solution

We are given: 2x+1+2x=482^{x+1} + 2^x = 48

Step 1: Use the property 2x+1=2⋅2x2^{x+1} = 2 \cdot 2^x: 2⋅2x+2x=48⇒3⋅2x=48⇒2x=483=162 \cdot 2^x + 2^x = 48 \Rightarrow 3 \cdot 2^x = 48 \Rightarrow 2^x = \frac{48}{3} = 16

Step 2: Solve for xx: 2x=16=24⇒x=42^x = 16 = 2^4 \Rightarrow \boxed{x = 4}

Exact answer: x=4\boxed{x = 4}

Approximate answer: x=4.000\boxed{x = 4.000}

Original worksheet page 2: question and worked solution for 1-9-010

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