# Natural Logarithm Easy QuestionsPlz help

## Main Question or Discussion Point

hello,

I was trying to figure out what will be the y value for this equations:

1 - e^-0.15*10^-5*y = 0.1

Could somebody help me in this??????????? The answer is supposed to be 70,240.

thanks.

gel
1 - e^-0.15*10^-5*y = 0.1
What does that mean?
1 - (e^-0.15)*(10^-5)*y = 0.1
1 - (e^-0.15)*(10^(-5*y)) = 0.1
1 - (((e^-0.15)*10)^-5)*y = 0.1
1 - e^(-0.15*(10^(-5*y))) = 0.1
1 - e^(-0.15*(10^-5)*y) = 0.1
1 - e^(-0.15*(10^(-5*y))) = 0.1

Sorry , i forgot to put the parenthesis. Here , it goes.. Hope it will be clear this time.

Note that the parameter lambda has this value:

lambda = (0.15*10^-5)

And i was trying to calculate,

(1 - e^(-lambda*y)) = 0.1 for y, and the answer is assumed to be 70,240.

Similarly,

1 - e^(-lambda*y) = 0.632, and the answer for this is supposed to be 666,667.

I am really confused how we get to this answer. I am not sure wether we use log or ln to get this answer.

thanks.

gel
well, ln(x) is the inverse of the exponential function exp(x) == e^x, so you must use that. Rearrange it so that you just have e^(something) on one side of the equation, and apply ln to both sides (actually mathematicians often use log to mean ln, but calculators use ln to mean natural log, log to mean base 10 log).

I tried, but not getting the right answer.

Could somebody clear this confusion...

thanks.

gel
Last edited by a moderator:
Thanks a lottttttttt gel...i got it right now.... :-)
The text contains a mathematical question with an equation and a provided answer, along with a similar equation and its answer. The user is seeking clarification on how to solve these equations.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Natural Logarithm Easy QuestionsPlz help

## Main Question or Discussion Point

hello,

I was trying to figure out what will be the y value for this equations:

1 - e^-0.15*10^-5*y = 0.1

Could somebody help me in this??????????? The answer is supposed to be 70,240.

thanks.

gel
1 - e^-0.15*10^-5*y = 0.1
What does that mean?
1 - (e^-0.15)*(10^-5)*y = 0.1
1 - (e^-0.15)*(10^(-5*y)) = 0.1
1 - (((e^-0.15)*10)^-5)*y = 0.1
1 - e^(-0.15*(10^(-5*y))) = 0.1
1 - e^(-0.15*(10^-5)*y) = 0.1
1 - e^(-0.15*(10^(-5*y))) = 0.1

Sorry , i forgot to put the parenthesis. Here , it goes.. Hope it will be clear this time.

Note that the parameter lambda has this value:

lambda = (0.15*10^-5)

And i was trying to calculate,

(1 - e^(-lambda*y)) = 0.1 for y, and the answer is assumed to be 70,240.

Similarly,

1 - e^(-lambda*y) = 0.632, and the answer for this is supposed to be 666,667.

I am really confused how we get to this answer. I am not sure wether we use log or ln to get this answer.

thanks.

gel
well, ln(x) is the inverse of the exponential function exp(x) == e^x, so you must use that. Rearrange it so that you just have e^(something) on one side of the equation, and apply ln to both sides (actually mathematicians often use log to mean ln, but calculators use ln to mean natural log, log to mean base 10 log).

I tried, but not getting the right answer.

Could somebody clear this confusion...

thanks.

gel
Last edited by a moderator:
Thanks a lottttttttt gel...i got it right now.... :-)
user
The text contains a mathematical question with an equation and a provided answer, along with a similar equation and its answer. The user is seeking clarification on how to solve these equations.

TYPE: SINGLE_QUESTION_WITH_ANSWER