lets solve the exponential equation 2e^x = 50. (a) first, we isolate e^x to get the equivalent equation 25…

lets solve the exponential equation 2e^x = 50. (a) first, we isolate e^x to get the equivalent equation 25 enter an equation. (b) next, we take in of each side to get the equivalent equation ln(25) (c) now we use a calculator to find x ≈ 3.219. (round your answer to three decimal places.) need help? read it

lets solve the exponential equation 2e^x = 50. (a) first, we isolate e^x to get the equivalent equation 25 enter an equation. (b) next, we take in of each side to get the equivalent equation ln(25) (c) now we use a calculator to find x ≈ 3.219. (round your answer to three decimal places.) need help? read it

Answer

Explanation:

Step1: Isolate $e^x$

Divide both sides of $2e^x = 50$ by 2. So $e^x=\frac{50}{2}=25$.

Step2: Apply natural - logarithm

Take the natural logarithm of both sides. Since $\ln(e^x)=x$, we get $x = \ln(25)$.

Step3: Calculate the value

Using a calculator, $\ln(25)\approx3.219$.

Answer:

(a) $e^x = 25$ (b) $x=\ln(25)$ (c) $3.219$