Question

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

Answer 1

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.

Answer 2

c) x = 1.15

Explanation:

`3e^(2x)+12=42`

Rearranging the equation

`\\\Rightarrow 3e^(2x)=42-12\\\Rightarrow 3e^(2x)=30\\\Rightarrow e^(2x)=(30)/(3)\\\Rightarrow e^(2x)=10`

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

`lne^(2x)=ln10\\\Rightarrow 2x=ln10\\\Rightarrow x=(ln10)/(2)\\\Rightarrow x=1.15129`

∴ x = 1.15