Log, Exponential Questions: 3e^x - 5 = -2e^{-x}, 2 ln(x) - 3 ln(1/x) = 10

[IshaanM8]

Hello visitors and maths geniuses.
I'm starting to learn logarithms and exponents.
I had pulled up some questions to do. These are the ones and they fall under "Non-Calculator".
I'm stuck and i don't even know where to start with these.

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Solve for x :

a. \(\displaystyle 3e^x\, -\, 5\, =\, -2e^{-x}\)

b. \(\displaystyle 2\, \ln(x)\, -\, 3\, \ln\left(\dfrac{1}{x}\right)\, =\, 10\)

---

Please help me in any way possible.
Thank you.

 

[Deleted member 4993]

Hello visitors and maths geniuses.
I'm starting to learn logarithms and exponents.
I had pulled up some questions to do. These are the ones and they fall under "Non-Calculator".
I'm stuck and i don't even know where to start with these.

---

Solve for x :

a. \(\displaystyle 3e^x\, -\, 5\, =\, -2e^{-x}\)

b. \(\displaystyle 2\, \ln(x)\, -\, 3\, \ln\left(\dfrac{1}{x}\right)\, =\, 10\)

---

Please help me in any way possible.
Thank you.

For problem a) :

Hint

e^(-x) = 1/e^(x)

For problem b) :

Hint:

c* ln(a) = ln(a^c) and

ln(a) - ln(b) = ln(a/b)

 

[Steven G]

Hello visitors and maths geniuses.
I'm starting to learn logarithms and exponents.
I had pulled up some questions to do. These are the ones and they fall under "Non-Calculator".
I'm stuck and i don't even know where to start with these.

---

Solve for x :

a. \(\displaystyle 3e^x\, -\, 5\, =\, -2e^{-x}\)

b. \(\displaystyle 2\, \ln(x)\, -\, 3\, \ln\left(\dfrac{1}{x}\right)\, =\, 10\)

---

Please help me in any way possible.
Thank you.

There are different ways to do these. For part a I would 1st multiply by e^x. Then I would let u = e^x and obtain a quadratic in terms of u. Solve for u and then for x.

Disclaimer: The use of u substitution has originally used by Denis who gets all credit for this method

 

[Deleted member 4993]

....Disclaimer: The use of u substitution has originally used by Denis who gets all credit for this method

But Jomo he is just a junior member (with ~ 600 posts) - and you are a senior member (with > 2000 psts).

So his discovery and usage cannot pre-date yours!!!

 

[IshaanM8]

Thanks for the tips.
I did some working around, using the substitution method and all.
I also used quadratic formula in order to get the solution.
I've achieved the answer for A and B. Thanks for the help!

 

[Steven G]

But Jomo he is just a junior member (with ~ 600 posts) - and you are a senior member (with > 2000 psts).

So his discovery and usage cannot pre-date yours!!!

Can I remove my post? PLEASE!