help with equation

cr771 said:
|3log10x-1|=2

i''ll be very greatful for your help
Click to expand...
I am assuming that you need to solve for 'x'.

How would you solve for 'x' given the following equation:

loga(x) = b​

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
what i did:

|3log(x-1)|=log100
|(x-1)^3|=100
|(x-1)^2|=10

is it correct?
 
cr771 said:
|3log10x-1|=2

i''ll be very greatful for your help
Click to expand...

Whatever you are taking the logarithm of (the argument), should be in €grouping
symbols, such as parentheses. Also, you should space out your characters as
follow for better readability/emphasis.

Did you intend | 3log10(x - 1) | = 2?

Or, did you intend | 3log10(x) - 1 | = 2?


P.S. I normally do not advocate for a space after the open absolute value bar and
before the close absolute value bar, but otherwise in this format, they are close
and look near like ones.
 
cr771 said:
It was stupid i know
Click to expand...
Let us unstupidify then!

It should have been:

|3log(x-1)| = 2

|log10(x-1)^3| = 2

|(x-1)^3| = 102....Incorrect.. Now you need to consider two signs (\(\displaystyle \pm \)) of [log10(x-1)^3](suggested in response #3)

\(\displaystyle \pm \)[log10(x-1)^3] = 2

log10(x-1)^3 = \(\displaystyle \pm \)2

(x-1)^3 = 100 .................. or............................. (x-1)^3 = \(\displaystyle \frac{1}{100}\)

continue.......................
 
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cr771 said:
what i did:

|3log(x-1)|=log100
|(x-1)^3|=100
|(x-1)^2|=10

is it correct?
Click to expand...
Looking just at the first two lines, I see that (a) this is a different problem than you originally stated, and (b) you got things out of order.

I would start this way:

[MATH]| 3\log(x-1) | = 2[/MATH]​
[MATH]3\log(x-1) = \pm 2[/MATH]​

then continue.

Taking your approach, you can't undo the log when it is not the last operation being done on the left. Rather,

[MATH]| 3\log(x-1) | = 2[/MATH]​
[MATH]| 3\log(x-1) | = \log(100)[/MATH]​
[MATH]\log(x-1)^3 = \pm \log(100)[/MATH]​

then continue.
 
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