Need someone to check my work

A

abel muroi

Junior Member
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Jan 13, 2015
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I was given the problem log5 (x + 1) - log5 (x - 1) = 2 and was told to solve for x

here is my work...

log5 (x + 1) - log5 (x - 1) = 2

log5 ((x+1)/(x-1)) = log525 .......( i took the log of 2)

(x+1)/(x-1) = 25............... (divided each side by log5)

x + 1 = 25x - 25 ............. (then i subtract each side by 1 and x)

26 = 24x

1083333333 = x

did i do this correctly?
 
abel muroi said:
I was given the problem log5 (x + 1) - log5 (x - 1) = 2 and was told to solve for x

here is my work...

log5 (x + 1) - log5 (x - 1) = 2

log5 ((x+1)/(x-1)) = log525 .......( i took the log of 2)

(x+1)/(x-1) = 25............... (divided each side by log5)

x + 1 = 25x - 25 ............. (then i subtract each side by 1 and x)

26 = 24x

1 . 083333333 = x ............. you are missing the decimal point.

did i do this correctly?
Click to expand...

You were advised to put your answer - back into the original equation and see if you come-up with an identity (Left-hand-side = Right-hand-side).

Did you follow that advice?
 
Last edited by a moderator:
Subhotosh Khan said:
You were advised to put your answer - back into the original equation and see if you come-up with an identity (Left-hand-side = Right-hand-side).

Did you follow that advice?
Click to expand...

I just did, and i keep getting 25.0000001

what did i do wrong?
 
use x = 13/12 instead of the decimal approximation.
 
Subhotosh Khan said:
Where did you get 25.0000001 - please show your work so that we can find out....
Click to expand...

log5 (x + 1) - log5 (x - 1) = 2

(1.083333333 + 1) - (1.083333333 - 1) = 2
(2.083333333) - (0.083333333) = 2
(2) = 2

nevermind i think i have figured it out.
 
Last edited:
abel muroi said:
log5 (x + 1) - log5 (x - 1) = 2

(1.083333333 + 1) - (1.083333333 - 1) = 2
(2.083333333) - (0.083333333) = 2
(2) = 2

nevermind i think i have figured it out.
Click to expand...
No, this check is all wrong. You are subtracting logs! What happened to the logs? For ANY value of x you have (x+1)-(x-1)=2!!!
In the original equation, replace x with1.083333333 and change NOTHING else.
log5 (1.083333333 + 1) - log5 (1.083333333 - 1) =? 2
log5 (2.083333333) - log5 (0.083333333) =? 2
log5 (2.083333333/0.083333333) =?2
log5 (25) =?2 YES!
 
Last edited:
Jomo said:
No, this check is all wrong. You are subtracting logs! What happened to the logs? For ANY value of x you have (x+1)-(x-1)=2!!!
In the original equation, replace x with1.083333333 and change NOTHING else.
log5 (1.083333333 + 1) - log5 (1.083333333 - 1) =? 2
log5 (2.083333333) - log5 (0.083333333) =? 2
log5 (2.083333333/0.083333333) =?2
log5 (25) =?2 YES!
Click to expand...
.thank you
 
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