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Chapter 3: Problem 20

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$4 e^{x}=91$$

Short Answer

Expert verified
The solution for \(x\) to three decimal places is approximately 3.000.

Step by step solution

01

Divide by constant

First, we have to isolate the exponent part \(e^x\). Therefore the equation \(4e^x = 91\) should be divided by 4. This gives us \(e^x = \frac{91}{4}\)
02

Apply Natural Logarithm

After having isolated the exponent, we now take the natural logarithm (ln) on both sides of the equation to get \(x\). The logarithm of an exponential number where base e (ln e) equals 1. So, we take natural logarithm on both sides of the equation to get \(x = ln(\frac{91}{4})\).
03

Compute Value

Now that we have the equation \(x = ln(\frac{91}{4})\), we just need to compute the value which equals about 2.9957 when rounded of up to 4 decimal places.

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