Equation problem

[Steel]

I have an equation 13.8 = 5 lg 1000r / 10 + r. I know this can be written as lg r = -0.2r + 0.76 but I cannot figure out how this is achieved. It's been forever since I've done any maths and honestly I seem to have forgotten a lot about what I learned at school

 

Could someone do a step by step demonstration of how to get from the first equation to the second so I would understand where the 'result' comes from. Thank you!

[insane_alien]

okay, i'll start you off.

 

hint: multiply both sides by 10+r

[Steel]

I'm still rather confused but I did get the correct result. Can you tell me if I've done it correctly or not?

 

13.8= 5 lg 1000r/10 + r

13.8 = 5 lg 100r + r

-5 lg 100r = r - 13.8

lg 100r = -0.2r + 2.76

2 lg r = -0.2r + 2.76

lg r = -0.2r + 2.76 - 2

lg r = -0.2r + 0.76

[Dc Nilbog]

Correct me if I am wrong, but I think what he meant was, well, consider this example:

 

To determine Y>

X = Y / 2

X*2 = Y

Y = X / 2

 

 

I hope that helped

 

Dc Nilbog

[the tree]

Correct me if I am wrong, but I think what he meant was, well, consider this example:

 

To determine Y>

X = Y / 2

X*2 = Y

Y = X / 2

 

 

I hope that helped

 

Dc Nilbog

WHAT

[insane_alien]

Correct me if I am wrong, but I think what he meant was, well, consider this example:

 

To determine Y>

X = Y / 2

X*2 = Y

Y = X / 2

 

 

I hope that helped

 

Dc Nilbog

 

:eek::eek::eek:

[Dc Nilbog]

Sorry I was meant to say:

 

To determine Y>

X = Y / 2

X*2 = Y

Y = X*2

 

But hey, it's the first step that was important right?

 

Dc Nilbog

[Country Boy]

I'm still rather confused but I did get the correct result. Can you tell me if I've done it correctly or not?

You posted a question, got one response that said "first multiply both sides by 10+ r" and just ignore it?

 

13.8= 5 lg 1000r/10 + r

Okay, first, do you really mean 13.8= 5 lg (1000r/10)+ r or 13.8= 5 (lg(1000r)/10)+ r or 13.8= 5 lg(1000r)/(10+ r)? insane alien was assuming you meant the last.

 

13.8 = 5 lg 100r + r

But this is true only if you mean the first.

-5 lg 100r = r - 13.8

lg 100r = -0.2r + 2.76

2 lg r = -0.2r + 2.76

Assuming you meant the first of the three options above, this is correct so far.

 

lg r = -0.2r + 2.76 - 2

No. "2 lg r" is 2 MULTIPLIED by lg r. The "inverse" of that is to DIVIDE by lg r, not subtract it.

lg r = -0.2r + 0.76