Step 3 003 ln 2 0 ln 1 03 ln 2 003 e t t 003 t 003 ln 2 ln 2 003 t Hint Use

Step 3 003 ln 2 0 ln 1 03 ln 2 003 e t t 003 t 003 ln

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Step 3: 0.03 ln 2 0. ln 1 03 ln 2 0.03 e t t = = 0.03 t 0.03 ln 2 ln 2 0.03 t = = Hint: Use your calculator to numerically evaluate your expression for x , and round your answer to the nearest millionth. Answer: ln 2 0.6931471806 0.03 0.0 23.104906 3 02 23.104906 t t = Example D Solve: 2 1 3 3 10 x x = . Express your answer exactly, in terms of logs, and also give a numerical approximation, accurate to the nearest millionth. Taking the natural log of both sides of the equation, we get: ( ) ( ) 2 1 3 2 1 3 3 10 3 1 ln 0 ln x x x x = = Now we can use the power rule, Property VI , once on each side of the equation, to pull down the exponents: ( ) ( ) ( ) ( ) 2 3 1 2 ln 3 ln 10 ln 3 l 0 3 n 1 1 x x x x = = Next we’ll solve for x . We start by using the distributive property to distribute the logs on each side of the equation: ( ) ( ) ln3 ln3 ln10 ln10 ln10 ln3 2 1 3 2 3 x x x x = = continued…
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