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when I googled the answer, i found out that m-cresol has a PKa value of 10.1 whereas phenol has 10.0.
I am simply unable to use any logic to compare their strengths.
We have been taught only the resonance effects and inductive effects (also exceptionally the ortho effect).
Here, none of these apply ! Steric hindrance doesn't come into the picture, too !
Based on what am I supposed to compare their basic strengths ?
The pKa of meta-cresol suggests that it is slightly less acidic than phenol. As commented, the difference is quite subtle. You could invoke the greater electronegativity of the carbon in methyl as compared to hydrogen, you can neglect any hyperconjugation, and you can simply dismiss it. What, really, is the significance of that tiny difference in pKa? You just keep invoking and/or dismissing the effects you have been taught until you come up with the "right" answer, the one that appears to explain the effect.
Or, to phrase the question differently, is there some difference between phenol and meta-cresol that might explain, or contribute to the slight difference in pKa? My first question is How significant are the numbers in the measurement? If you Google the pKa of phenol, on the first page of hits, you can find 9.88, 9.95, 9.98, 9.99, 10 (no decimal), and ~10 (with roughly sign). If you do the same for meta-cresol, you get 10.09, 10.1 and 10.13. So the various numbers (and there may be more) indicate a range of uncertainty.
My second question is What other differences are there? Melting point, solubility... Phenol is a solid at room temperature, mp = 40.5$^o$C. But with 11% H2O, it is liquid. Meta-cresol is liquid, mp = 11$^o$C. It is difficult to turn these facts into an explanation, but there is something interesting about the solubilities. Meta-cresol is soluble in water 23.5 g/L at 20$^o$C, 58g/L at 100$^o$C. Even tho it is liquid at room temperature, it is not completely miscible in water even at 100$^o$C. On the other hand, phenol is more soluble in water at room temperature (83 g/L at 20$^o$C), liquid with addition of 11% water, and miscible above its melting point.
These little bits of information suggest that phenol is more highly hydrated in water. Except for that extra lattice energy that makes it a solid, phenol solubility in water would appear dramatically different from meta-cresol. Imagine that room temperature is about 42$^o$C (a bit warm). Phenol is liquid, miscible with water; meta-cresol is liquid, not very soluble in water (~3-4%).
So now we ought to consider hydration effects in addition to the standard inductive and resonance effects. Among the three, one is likely to be able to explain the tiny difference.
Perhaps a fair answer would be that resonance effects are nil because the methyl is in the meta position. Although the carbon is electron withdrawing relative to hydrogen, the methyl group (sp$^3$) is less electronegative than the ring carbon (sp$^2$), and has more electrons to donate, so the negative charge on oxygen has less room to expand in. And the fact that phenol is better hydrated suggests the H2O molecules are helping phenolate spread the charge more than they help meta-cresolate.
And your teacher will appreciate such a long-winded discussion of all the effects you can possibly think of.
