Logarithm problem, differences

[matxjos]

I feel so dumb. I cannot figure out this relationship for the life of me.pH= -log[H+]

Imagine 2 concentrations. If the hydronium ([H+]) concentration differs by a factor of 2, it means the pH of the 2 solutions differs by -log √2

HOW?!
So basically, what they're saying is
(logx)(log√2)=log2x

HOW?

 

[jedishrfu]

where did you get the sqrt(2) from?

they actually differ by the log(2).

2 * 0.05 = 0.1 and in log form: log(2) + log(0.05) = log(0.1)

hence log(2) = log(0.1) - log(0.05)

 

[matxjos]

where did you get the sqrt(2) from?

they actually differ by the log(2).

2 * 0.05 = 0.1 and in log form: log(2) + log(0.05) = log(0.1)

hence log(2) = log(0.1) - log(0.05)

Okay...after more thought, I am convinced my solutions manual is wrong. I hate how many errors are in these things. Thanks jedishrfu.