Tathmini kwa kutumia tabia za logariti: 3/(69.8)

Haya hapa majibu ya maswali yako:

1. Tumia jedwali za logariti kwa usahihi hadi tarakimu 4 muhimu kutathmini: $\sqrt[3]{\frac{0.07214 \times 2.037}{69.8}}$

• Hatua ya 1: Weka usemi kama $x$ na utumie logariti.

  $$x = \sqrt[3]{\frac{0.07214 \times 2.037}{69.8}}$$ $$\log_{10} x = \frac{1}{3} \left( \log_{10}(0.07214) + \log_{10}(2.037) - \log_{10}(69.8) \right)$$

• Hatua ya 2: Tafuta logariti za nambari kutoka jedwali.

  $$\log_{10}(0.07214) = \bar{2}.8582$$ $$\log_{10}(2.037) = 0.3090$$ $$\log_{10}(69.8) = 1.8439$$

• Hatua ya 3: Fanya hesabu za logariti. Kwanza, ongeza logariti za nambari kwenye kiasi:

  $$\log_{10}(0.07214) + \log_{10}(2.037) = \bar{2}.8582 + 0.3090 = \bar{1}.1672$$

  Kisha, toa logariti ya kigawanyo:

  $$\bar{1}.1672 - 1.8439 = (-1 + 0.1672) - (1 + 0.8439)$$ $$= -1 + 0.1672 - 1 - 0.8439$$ $$= -2 - 0.6767 = -2.6767$$

• Hatua ya 4: Gawanya kwa 3.

  $$\log_{10} x = \frac{-2.6767}{3} = -0.892233...$$

• **Hatua ya 5: Badil