I will be of no help with the 2nd ?, but for your question about why the answer for the first is that: Basically, an acid essentially gives up hydrogen. Therefore, the more acidic, ie the lower the ph, the greater the amount of hydrogen ions you'll find in the soil. Hope that explanation makes sense.
1. pH is determined by the amount of "free" hydrogen ions [H+] such that the MORE [H+] something has, the LOWER the pH (as noted by your equation ph=-log[H+]). By saying "not less than", the question is actually saying, "at least or higher" so think of your final answer as saying "this soil needs this much [H+] or MORE," which translates to "this soil's pH needs to be this or LESS." Another note on significant figures since this is chem, note that the question gave this number, "1.58 x 10⁻⁸...," which comes out to 2 significant figures (2 places after the decimal point) so your final answer needs to follow the same convention meaning it should be pH</=7.80
2. By law, a natural log cannot equal to a negative value (unless you include imaginary numbers, but that is a different story), hence adding the zero to the left to signify that.
ya so im stupid so im asking for help again, i think the first question is easier to understand if you took/have chemistry.
1) Siberian irises flourish when the concentration of hydrogen ions [H+] in the soil is not less than 1.58 x 10⁻⁸ mole per liter. What is the pH of the soil in which these irises will flourish?
ph=-log[H+]
okay so the answer according to the answer key i found online is 7.8013 OR LESS, i somehow managed to get that answer (probably because i was influenced by seeing the answer before solving). my concern is why is it 'OR LESS'? shouldn't it be 'OR MORE'? since the question said "not less than" which basically means more right??
2) Inequalites with logarithms: this is an example from my worksheet.
ln(4x-1)<2
ln(4x-1)<2
eˡⁿ⁽⁴ˣ⁻¹⁾<e²
0<4x-1<e²
1<4x<e²+1
¼<x<²(e²+1)
0.25<x<2.0973
on the fourth line, where did the '0<...' come from??