Simple log question

Tar.Aldarion

I forget the easiest process to solve this. Any help appreciated.

.0615log10(29+400x/530+18x) = -.07

Michael Collins

1) Divide both sides by that log coefficient

2) Take the antilog of both sides i.e. exponentiate both sides with a base of ten - this will get rid of the log on the left.

3) Solve for x.

Dufresne

Exactly as Michael said, x is working out at about -1.53

Tar.Aldarion

Thanks Michael, I was doing that but kept leaving out the - and getting a crazy answer. Cheers! This is for the sodium levels in a person.

The answer is .02396... Dufresne. :-)

Dufresne

Hi Tar - I just double checked that and got the same answer as before - I presumed the 10 you had after the word log meant log to the base 10 - if not sorry.

Michael Collins

Dufresne wrote: »

Hi Tar - I just double checked that and got the same answer as before - I presumed the 10 you had after the word log meant log to the base 10 - if not sorry.

So did I actually. If it isn't 10 then when you come to using the antilog you have to use the same base. I don't see myself how you get 0.02396 as the answer. Are we both solving the same problem?

.0615log10(29+400x/530+18x) = -.07

Tar.Aldarion

Yes, the same question.
When I say log 10, I mean the log button on my calculator. Which is to the base 10 by default yes? So yes, base 10.
I used 10^x for antilog.
I knew the answer from the other method I did so I know that I was meant to get .02...


I'm not sure what you are doing, I may have explained it wrong. I should have just said 'log' and not 'log10'

Tar.Aldarion

.0615log10(29+400x/530+18x) = -.07

=> log10(29+400x/530+18x) = -1.138211382
=> (29+400x/530+18x) = .072742566
=> 1.309366191x + 38.55356 = 29 + 400x
=> 9.55356 = 398.6906338x
=> x = .023962338

if not sorry.

Don't be silly!
Thanks for the help.

Dufresne

Yeah I see what happened - I took .0615log10(29+400x/530+18x) = -.07 literally as you typed it and you really meant .0615log10((29+400x)/(530+18x))= -.07

The way you have it typed just looked like only the 400x was divided by the 530. I had too much time on my hands today - Sorry for all the confusion


Just checked that and of course it gives x=0.02396

Tar.Aldarion

Whoops! Sorry about that. I shouldn't just copy stuff from my A4 pad without checking over it. Thanks for wasting your time. :-)

Michael Collins

Yeh I took it the same way as Dufresne. I guessed something was a bit off with it since you could just add the to x terms together: 400x/530+18x if you take it the literal way.

Pherekydes

Yay for LaTeX.

Code: [EQ] \ .0615 log_{10} \left(\frac{29+400 x}{530+18x}\right)= -.07 [/EQ]

Mathbin

Tar.Aldarion

Nice.