Question

What is the solution to the equation below?round your answer to two decimal places 3e^2x+ 12 =42

Answer 1

Answer:

c) x = 1.15

Step-by-step explanation:

$3e^{2x}+12=42$

Rearranging the equation

$\\\Rightarrow 3e^{2x}=42-12\\\Rightarrow 3e^{2x}=30\\\Rightarrow e^{2x}=\frac{30}{3}\\\Rightarrow e^{2x}=10$

Taking natural logarithm on both sides because $lne^x=x$

$lne^{2x}=ln10\\\Rightarrow 2x=ln10\\\Rightarrow x=\frac{ln10}{2}\\\Rightarrow x=1.15129$

∴ x = 1.15

Answer 2

E^2x=(42-12)/3, that is easy
Then, the magic!
Ln(e^2x)=Ln[(42-12)/3]
2x.Ln(e)=Ln[(42-12)/3]. "Ln(e)=1"
X={Ln[(42-12)/3]}/2
Good luck!
M.