How do you solve $20 (100 - e^{\frac{x}{2}}) = 500$ $20 (100 - e^(x/2)) = 500$ ?

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How do you solve $20 (100 - e^{\frac{x}{2}}) = 500$ $20 (100 - e^(x/2)) = 500$ ?

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Answer 1 · 2015-08-06T17:24:27

$x = log (5625) = 3.75$ $x=log(5625)=3.75$ 2 d.p.

Explanation:

Rearrange the expression as follows:

$20 (100 - e^{\frac{x}{2}}) = 500$ $20(100-e^(x/2))=500$ => $e^{\frac{x}{2}} = 75$ $e^(x/2)=75$

Take logarithms =f both sides:

${log e}^{\frac{x}{2}} = \frac{x}{2} = log (75)$ $loge^(x/2)=x/2=log(75)$ => $x = 2 log (75) = log (75^{2}) = log (5625)$ $x=2log(75)=log(75^2)=log(5625)$

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How do you solve $20 (100 - e^{\frac{x}{2}}) = 500$ $20 (100 - e^(x/2)) = 500$ ?

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