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C3 - Logs help

Need some help with the following question. I don't know how to do it :redface:

3^x e^(7x+2)=15

mm it is supposed to be e^(7x+2) not sure how you latex that.

Any help would be appreciated :smile:

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Reply 1

MathMeister

My knowledge only extends to C2. I'm trying to understand concepts now. Dif/int are easy but understanding them is problematical. Shouldn't be too hard.

Reply 2

Super199

Original post by MathMeister

My knowledge only extends to C2. I'm trying to understand concepts now. Dif/int are easy but understanding them is problematical. Shouldn't be too hard.

Your point is?

Reply 3

rayquaza17

Original post by Super199

Need some help with the following question. I don't know how to do it :redface:

3^x e^(7x+2)=15

mm it is supposed to be e^(7x+2) not sure how you latex that.

Any help would be appreciated :smile:

Does this help:

3^{x}=e^{ln(3^{x})}=e^{xln(3)}

Reply 4

Super199

Original post by rayquaza17

Does this help:

3^{x}=e^{ln(3^{x})}=e^{xln(3)}

Nope

I honestly don't know what do with that.
Can I just take ln of both side and use log laws?

Reply 5

MathMeister

Original post by Super199

Your point is?

I just wanted to comment :/ I hope you do well in your exams.

Reply 6

Super199

Original post by MathMeister

I just wanted to comment :/ I hope you do well in your exams.

Haha fair enough. Stop procrastinating and go do some C1 :tongue:

Reply 7

Super199

Original post by MathMeister

Doing c2 at the mo. C1 doesn't test me much. I've basically done it all tbh.

Are you doing S1 or M1 next year?

Reply 8

MathMeister

I'm doing C1,C2,S1- FP1, M1 and M2. (I think) Or instead it will be S2 rather than M2.

Reply 9

CTArsenal

Original post by Super199

Any help would be appreciated :smile:

Okay so

3^x e^{7x+2} = 15

I would natural log both sides, so you have:

\ln(3^x e^{7x+2}) = \ln(15)

Use your rules of logarithms to get this:

\ln(3^x) + \ln(e^{7x+2}) = \ln(15)

I'm sure you can do the rest bearing in mind the logarithm rule of

\ln(a^b) = b\ln(a)

and rearranging.

(edited 9 years ago)

Reply 10

shutupem

Original post by Super199

Need some help with the following question. I don't know how to do it :redface:

3^x e^(7x+2)=15

mm it is supposed to be e^(7x+2) not sure how you latex that.

Any help would be appreciated :smile:

ln(3^x) + ln(e^(7x+2) = ln15[br]xln3 + 7x + 2 = ln15

as lne = 1 and ln(e^(7x+2)) = (7x+2)lne

xln3 + 7x = ln15 - 2[br]x(ln3 + 7) = -2 + ln15[br]x = (-2 + ln15)/(ln3+7)

that's what I'd do anyway

Reply 11

Super199

Original post by CTArsenal

Okay so

3^x e^{7x+2} = 15

I would natural log both sides, so you have:

\ln(3^x e^{7x+2}) = \ln(15)

Use your rules of logarithms to get this:

\ln(3^x) + \ln(e^{7x+2}) = \ln(15)

I'm sure you can do the rest bearing in mind the logarithm rule of

\ln(a^b) = b\ln(a)

and rearranging.

Ahh got it. Didn't spot the 2nd step :rolleyes:

. Thanks

Reply 12

Super199

Original post by shutupem

ln(3^x) + ln(e^(7x+2) = ln15[br]xln3 + 7x + 2 = ln15

as lne = 1 and ln(e^(7x+2)) = (7x+2)lne

xln3 + 7x = ln15 - 2[br]x(ln3 + 7) = -2 + ln15[br]x = (-2 + ln15)/(ln3+7)

that's what I'd do anyway

Yh that's what I got with a bit of guidance :tongue:

. Cheers

(edited 9 years ago)

Reply 13

the bear

Original post by Super199

Need some help with the following question. I don't know how to do it :redface:

3^x e^(7x+2)=15

mm it is supposed to be e^(7x+2) not sure how you latex that.

Any help would be appreciated :smile:

e^{(7x + 2)}

e[sup](7x + 2)[/sup

just type in the above & put the missing square bracket...

Reply 14

rayquaza17

Original post by shutupem

ln(3^x) + ln(e^(7x+2) = ln15[br]xln3 + 7x + 2 = ln15

as lne = 1 and ln(e^(7x+2)) = (7x+2)lne

xln3 + 7x = ln15 - 2[br]x(ln3 + 7) = -2 + ln15[br]x = (-2 + ln15)/(ln3+7)

that's what I'd do anyway

Full solutions should be a last resort.

Reply 15

sharvarivadeyar

Original post by Super199

Need some help with the following question. I don't know how to do it :redface:

3^x e^(7x+2)=15

mm it is supposed to be e^(7x+2) not sure how you latex that.

Any help would be appreciated :smile:

sorry if this is terribly silly of me but are you solving for x?
usually in that case i take ln on both sides and use the properties! but im not getting e^(7x+2)...

Reply 16

Super199

Original post by sharvarivadeyar

sorry if this is terribly silly of me but are you solving for x?
usually in that case i take ln on both sides and use the properties! but im not getting e^(7x+2)...

I'm not sure what your question is? If you are referring to the e^(7x+2) bit underneath the question, I was saying that I couldn't type it in properly. The answer isn't that :tongue:

Reply 17

sharvarivadeyar

Original post by Super199

I'm not sure what your question is? If you are referring to the e^(7x+2) bit underneath the question, I was saying that I couldn't type it in properly. The answer isn't that :tongue:

lolol nvm got it xD sorry!