Math Is Fun Forum

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Simultaneous Logarithms

Hi All

In the past week I have been learning logarithms for the first time and so far it has all been good, until
I came across the following 2 equations right at the end. The problem I have with the first is that none
of the others have add/sub operations in the brackets. And the second is a simultaneous solve and I am
not sure how to approach it.

Here are the offending articles..

   Give 2 integer values for n.

and the system is as follows

Give values for both x and y.

On the first, I am not sure where to begin. I have tried a few different things and just seem
to get in a muddle.

on the Second if I expand the top one out to

and then there would be equal coefficients, but I don't know
if the bottom is multiplied together? There is no operation specified, if it is multiply can I still cancel
it out and subtract the remaining parts?

All help as always, very gratefully appreciated.

Thanks
David

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Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Simultaneous Logarithms

Hi;

Does that help a little or do you need more.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Simultaneous Logarithms

Hi Bobby

The answers in the back of the book ask for numerial solutions for n, apparently they are 2 and 4.

---

Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Simultaneous Logarithms

Can you get it from what I gave you? Or do you need the next step. Those answers are correct.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Simultaneous Logarithms

I'm just about to sit down for dinner, I'll have a go in a short while and get back to you on that

Thank you.

---

Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Simultaneous Logarithms

Hi Dave;

Okay, enjoy your dinner, I will have the next one ready for you.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Simultaneous Logarithms

Hi Bobby

I've got to get Emma ready for bed, she's already late. Gone 8PM here, (late enough for a 2 year old girl)
so I'll have to leave it until the morning.

Hard work, trying to learn math and bringing up a toddler

Talk soon and night night.

David

---

Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Simultaneous Logarithms

Cool, I need more time anyway.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Simultaneous Logarithms

Morning Bobby

i've worked through the solution you gave

->

->

is it reasonable to remove the fraction by multiplication

->

do I have to expand the LHS and RHS and subtract

from the RHS.

I really want to work this out, but every now and then I get stuck like this.
Sorry

---

Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Simultaneous Logarithms

Hi Dave;

Hold it, that is not what I meant.

I haven't been clear look in next move, just solve that. No Logs required.

Solve for n

n =2 and n = 4

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Simultaneous Logarithms

Hi Bobby

Got it..

In the book for the course there is no mention of disregarding the logs and just working the equations.
It makes a huge emphasis on the use of the indices laws and lots of questions using that and then
throws curve balls like this one, still it is good that it does.

I suppose it stops you from becoming complacent and thinking you can breeze through.

Thank you Bobby.

I'll have a go at the Simultaneous one now.

---

Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Simultaneous Logarithms

Hi Dave;

You have to manipulate it first using log laws to get it into post #2. That is what they mean , I think. After that you can just solve for what is inside of the logs.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Simultaneous Logarithms

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