basic log rule

[cherishablegirl]

Hi everyone,
this is just a really basic log question but I just wanted to understand the reasoning behind it

I know the rule log(AB) = log(A) + log(B)
but when I have a negative sign in front of the log, what happens?

I need to do simple logs for an exam to calculate things like pH, and I can't use a calculator, so I want to make sure I understand

I know the working out for this:

pH = -log (1.4x10^-4)
= -log 1.4 - log 10^-4
= -0.15 + 4
there pH = 3.93

but I'm confused why the logs are subtracted not added given the log(AB) = log(A) + log (B) rule.

Thank you!!

 

[Deleted member 4993]

Hi everyone,
this is just a really basic log question but I just wanted to understand the reasoning behind it

I know the rule log(AB) = log(A) + log(B)
but when I have a negative sign in front of the log, what happens?

I need to do simple logs for an exam to calculate things like pH, and I can't use a calculator, so I want to make sure I understand

I know the working out for this:

pH = -log (1.4x10^-4) = -[log(1.4) + log(10^-4)]
= -log 1.4 - log 10^-4
= -0.15 + 4
there pH = 3.93

but I'm confused why the logs are subtracted not added given the log(AB) = log(A) + log (B) rule.

Thank you!!

Those logs are being added - with a negative sign in front.

but the pH should be = -0.146 + 4 = 3.854

However, to calculate log(1.4) - you would need a calculator or log-table.

 

[cherishablegirl]

Thank you. Sorry I actually wrote the problem wrong, there was also a + log (0.12/0.10) to equal 3.93. But now I see how they do it. Thanks

 

[cherishablegirl]

so really it is this right?

pH = -log (1.4 x 10^-4)
= -[log(1.4) + log(10^-4)]
= -[ (0.15 + (-4) ]
= -(-3.85)
= 3.85

(i know this is just simple algebra now, i'm sorry)

 

[JeffM]

so really it is this right?

pH = -log (1.4 x 10^-4)
= -[log(1.4) + log(10^-4)]
= -[ (0.15 + (-4) ]
= -(-3.85)
= 3.85

(i know this is just simple algebra now, i'm sorry)

If you take it step by step, you won't go wrong.

\(\displaystyle -log\{1.4 * 10^{-4}\} = - \{log(10^{-4}) + log(1.4)\} = -\ \{(- 4) * log(10) + log(1.4)\} = - \{(-4) * 1 + log(1.4)\} \approx -\ (-\ 4 + 0.146) = \)

\(\displaystyle 4 - 0.146 = 3.854.\)

Many, many errors in algebra come from skipping steps. If you are at all unsure, don't skip steps.

 

[Dale10101]

Hi everyone,
this is just a really basic log question but I just wanted to understand the reasoning behind it

I know the rule log(AB) = log(A) + log(B)
but when I have a negative sign in front of the log, what happens?

I need to do simple logs for an exam to calculate things like pH, and I can't use a calculator, so I want to make sure I understand

I know the working out for this:

pH = -log (1.4x10^-4)
= -log 1.4 - log 10^-4
= -0.15 + 4
there pH = 3.93

but I'm confused why the logs are subtracted not added given the log(AB) = log(A) + log (B) rule.

Thank you!!

So, to emphasize the answer to you question, you CAN add the logs and then apply the last negation to their sum (the step that you skipped between your first and second step), OR you can distribute the outside negative sign as you mentally did to get the same result.

So, how would you check your answer and thereby have a better appreciation of what a log is and what it's inverse delivers? That is, given the pH of a solution what is its concentration? Might be good to know.