What is the hydronium ion concentration of a solution whose pH is 4.12?

By definition, #pH=-log_10[H_3O^+]#, and this represents a measure of the concentration of the hydronium ion, conceived to be the characteristic cation of water. We can also develop a #pOH# function, where #pOH=-log_10[HO^-]#. In water, under standard conditions, #pH+pOH=14#.

Historically, before the days of electronic calculators, log tables were habitually used by chemists, and mathematicians, and engineers, and students because logarithmic functions allowed fairly speedy calculation of products and quotients.

AS a bit of background, when we write #log_(a)b=c#, this means that #a^c=b#.

And thus ...............................................................

#log_(10)0.1=-1; log_(10)1=0; log_(10)10=1; log_(10)100=2; log_(10)1000=3#.

Note that you still have to plug that value into a calculator, and raise #10# to that power...........

See here for a similar spray.

Take the formula:
#pH = -log[H^+]#
and isolate #[H^+]#. You should get:

#[H^+] = 10^(-pH)#

#[H^+] = 10^(-4.12)#

#[H^+] = 0.000075858M#

Since yo only have 3 sig figs the answer would be:

#[H^+] = 7.59 * 10^(-5)M#