I know the very basic principles of logs

[lloydowen]

Homework Statement

I'm new to logs. I know the very basic principles of logs, unfortunately my notes are not helping my on this occasion. What I have so far is Solve the value 'x'

Homework Equations

6^(x+3)=56.34

The Attempt at a Solution

Here's what I have done, and I'm not sure where to go from here so could someone explain?

log6^(x+3)=log5.34
(x+3)log6=log56.34
(x+3)log6=1.751
------

Not sure if I've done it correctly, and I'm not sure where to go from next :/

If you have seen me asking a lot of questions tonight, I have an exam next week and I'm just getting ready for it :)

 

[micromass]

Good. Now you have an equation of the form

$$(x+3)b=c$$

Solve for x.

 

[lloydowen]

$$(x+3)b=c$$

Solve for x.

So, the next line would be xlog6 +3log6 = 1.751

Yes or no?

 

[BruceW]

I'm guessing on your first line, you meant log56.34 (since that's what you put on the next line, which is correct).

You have got it right so far. From here, its simple rearrangement to get x.

Edit: Sorry, I started writing this before micromass posted, so I am a little behind here.

yes, that would be the next line (although you could instead have divided both sides by b), but you get the right answer either way.

 

[micromass]

So, the next line would be xlog6 +3log6 = 1.751

Yes or no?

Yes.

 

[Mark44]

Here's what I have done, and I'm not sure where to go from here so could someone explain?

log6^(x+3)=log5.34
(x+3)log6=log56.34
(x+3)log6=1.751
------

As already noted, the first line above has a typo.

So, the next line would be xlog6 +3log6 = 1.751

Yes or no?

Yes.

As an alternative, starting from (x + 3)log(6) = log(56.34),
you could divide both sides by log(6) to get x + 3 = log(56.34)/log(6), and you can solve for x from there.

Note that put back in log(56.34) instead of using your value of 1.751. You'll get a more precise result if you DON'T put in rounded intermediate values. If you use the full values that your calculator gives you, you'll get answers that don't have built-in inaccuracies.

 

[lloydowen]

So, on that last line I done... xlog6 + 3log6

Do I (on a calculator) type log6= then Ans*3... and then add it to log6 ? I'm confused now :(

 

[lloydowen]

Any help guys? I'm real stuck ! Can't move on from here...

 

[lloydowen]

So I couldn't do multiplication method so I went for division.. Here's what I got.

(x+3=1.751)/log6

Uhh doesn't look right but is it ?

 

[micromass]

I really don't know what is bothering you so much. Can you solve

$$2(x+3)=5$$

??

The equation you list is the same thing but with different numbers.

 

[lloydowen]

So I think I have a final answer, I kept simplifying down. after that previous line i got (x=1.751)/log6 (-3)

Which then gave me a final answer of -0.75 to 2dp

 

[lloydowen]

New Question!

So I got another Question because I didn't full click with that last one..

75.2^x = 10.5 ^(3x-5)What I got so far...

log75.2^x=log10.5^(3x-5)
xlog75.2 = (3x-5)log10.5

Trying the next line... Suppose its the same as last time but the other way around?

Edit:
$$(xlog75.2=3x-5)/log10.5$$

 

[BruceW]

You got the last question right, with -0.75.

For the new question, you have got the use of logarithm correct. Now it is just a case of rearranging.

 

[lloydowen]

The new question I re-wrote the equation like so, $$xlog75.2 = 3xlog10.5-5log10.5$$ Is that wrong and/or a better method than the last way?

 

[Mark44]

The new question I re-wrote the equation like so, $$xlog75.2 = 3xlog10.5-5log10.5$$ Is that wrong and/or a better method than the last way?

You're not done yet. Add -3xlog(10.5) to both sides. Then on the left side, you'll have two terms with a factor of x. Factor the two terms into x(...other stuff) = <stuff on the right side>.

 

[cepheid]

You cannot put equals signs inside of expressions within parentheses. It makes no sense.

 

[lloydowen]

You cannot put equals signs inside of expressions within parentheses. It makes no sense.

Sorry, not quite sure what you mean here?

You're not done yet. Add -3xlog(10.5) to both sides. Then on the left side, you'll have two terms with a factor of x. Factor the two terms into x(...other stuff) = <stuff on the right side>.

Thanks for your help Mark, but I'm still unsure now :( Would it look like this..
$$(-3xlog(10.5)xlog75.2=-3xlog(10.5) 3x-5) / log10.5$$

Or $$((-3xlog(10.5)xlog75.2=(3xlog(10.5))3xlog10.5-5log10.5)$$ CONFUSED ! :(

 

[cepheid]

Sorry, not quite sure what you mean here?

I was talking about this:

$$(xlog75.2=3x-5)/log10.5$$

You have an equals sign inside the parentheses. It makes no sense.

 

[BruceW]

You have an equals sign inside the parentheses. It makes no sense.

haha, yeah, I think he means 'divide both sides by log10.5'

Edit: I don't know if that is allowable notation in maths, but you can see what he means by it.

 

[BruceW]

CONFUSED ! :(

Think it through yourself, you've done the hard bit already, you just needed to rearrange to get x as the subject of the formula.

 

[BruceW]

The new question I re-wrote the equation like so, $$xlog75.2 = 3xlog10.5-5log10.5$$ Is that wrong and/or a better method than the last way?

This bit is correct. Just think of the numbers as letters, you have something like: $ax = 3bx - 5b$, which is elementary algebra.

 

[lloydowen]

This bit is correct. Just think of the numbers as letters, you have something like: $ax = 3bx - 5b$, which is elementary algebra.

Ok... Thanks, I'll have another go now, My brain is fried haha!

 

[BruceW]

No worries, I know the feeling

 

[lloydowen]

I really don't see what I can do here, nothing seems to look right! I can see on your equation it would be $$(x=3bx-5b)/a$$ but I just can't see how to apply that to my equation :(

 

[BruceW]

Your equation is $xlog(75.2)=3xlog(10.5) - 5log(10.5)$ So you could also write it as $ax=bx+c$ if you wanted. You can choose how to define your constants.

You don't even need to write it as algebraic letters. You could just write down the actual numbers straight away, then find what x must be.

 

[lloydowen]

So I should put the $$-5log(10.5)$$ onto the left side, and cancel down? So I would be left with $$xlog(75.2)=3xlog(10.5)$$ Or should I divide the right hand side by $$log(75.2)$$ to get $$x$$ on it's own? I don't think I've been taught this properly :/

 

[BruceW]

hmm, I think you should practise more at this kind of stuff then. Because it can come up a lot. Its called 'rearranging to get something as the subject of the formula', or 'collecting like terms', or could be called 'solving the equation'. Do you have a maths textbook? Looking through it again might help.

There are essentially a few rules you have to stick to when you're rearranging an equation. You can do things like 'multiply both sides by the same thing' and 'add something to both sides' I'm guessing you're familiar with these?

Using these rules, you cannot turn the equation $xlog(75.2)=3xlog(10.5)-5log(10.5)$ into the equation $xlog(75.2)=3xlog(10.5)$

 

[lloydowen]

hmm, I think you should practise more at this kind of stuff then. Because it can come up a lot. Its called 'rearranging to get something as the subject of the formula', or 'collecting like terms', or could be called 'solving the equation'. Do you have a maths textbook? Looking through it again might help.

There are essentially a few rules you have to stick to when you're rearranging an equation. You can do things like 'multiply both sides by the same thing' and 'add something to both sides' I'm guessing you're familiar with these?

Using these rules, you cannot turn the equation $xlog(75.2)=3xlog(10.5)-5log(10.5)$ into the equation $xlog(75.2)=3xlog(10.5)$

I am familiar with those yes, but where I am taught a tutor will go through a subject/topic and then "its upto you to learn it" but I try my best to learn things myself but it's really quite hard for me to understand... and I don't have a Maths textbook, only class notes, do you recommened a book I get?

I know what I have to do I just struggle to see how I do it, or struggle to find the next step? It's hard to explain really, but when I 'click' I can do the questions all the time, just having trouble with these ones :(

 

[Mark44]

I really don't see what I can do here, nothing seems to look right! I can see on your equation it would be $$(x=3bx-5b)/a$$ but I just can't see how to apply that to my equation :(

Again, it makes no sense to write an equals in the middle of a parenthesized expression.

Here are the steps, starting from ax = 3bx−5b
ax - 3bx = -5b ; add -3bx to both sides
x(a - 3b) = -5b ; bring out common factor

x = -5b/(a - 3b) ; divide both sides by a - 3b

If you are trying to learn this without a textbook, that's not a good idea. I don't have any particular book to recommend, but there's a website that has tutorials in many different areas of mathematics, and this might be helpful - khanacademy.org.

 

[lloydowen]

Thank you for that! Tomorrow I'll get around to look that site and some online tutorials, I have tried them before but I've never really had much luck. Anyway good night from me, it's pretty late right now! :) Thanks for all your help guys !