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Maya_01's avatar

Natural logarithm?

Asked by Maya_01 (489points) June 15th, 2023 from iPhone

I have this friend who does acceleration maths. She is in the grade below me and she asked me a maths related question.
It’s concerning natural logarithm and my memory is a little rusty because I learnt this content approximately 2 years ago.
Can anyone explain to me the steps. She sent me her working out but she doesn’t understand how to get to the answer.

The question:
4e^-2x=1

Working out:
e^-2x=¼
-2x=ln(¼)—> i dont get what to do after this step 
 
The answer is:
x=ln(2)

Note: I know that people usually don’t answer homework related questions but this is a question for a friend and it’s concerning the logic behind natural logarithm.

I would really appreciate some help.
Thank you

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6 Answers

Maya_01's avatar

I know the answer I would just like some reasoning behind the logic.
So basically I am just asking for an explanation on how to get from
-2x=ln(¼) to x=ln(2)

Would really appreciate your help

Maya_01 (489points)“Great Answer” (1points) Flag as…
snowberry's avatar

Hey, come on guys! please help. This question is properly written, and I bet at least one of you can help.

snowberry (27929points)“Great Answer” (1points) Flag as…
Response moderated
Response moderated
janbb's avatar

I don’t have a clue but I sent it to LostinParadise who should be able to help.

janbb (63258points)“Great Answer” (0points) Flag as…
Maya_01's avatar

I appreciate the help I got.

Me and my friend eventually solved it.
Below I will show my working out so in the future it may help someone else.

4e^-2x=1
e^-2x=¼
loge(¼)=-2x
ln(¼)=-2x
ln(4^-1)=-2x
-1xln(4)=-2x
ln(4)=2x
x=ln(4)/2
x=½xln(4)
x=ln(4^½)
x=ln(2)

Maya_01 (489points)“Great Answer” (2points) Flag as…

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