Lutasin ang 30=75e^-0.002t

$$30 = 75 e ^ { - 0.002 t }$$

I-solve ang t

$$t=\ln(9332636185032188789900895447238171696170914463717080246217143397959669109757756344544403270978811023595949899303242426242154875213540323948415208172039307562344106661383251502739950759859018315111004.90796265113118240512514795933790805178271125415103810698378854426481119469814228660959222017662910442798456169448887147466528006328368452647429261829862165202793195289493607117850663668741065439805530718136320599844826041954101213229629869502194514609904214608668361244792952034826864617657926916047420065936389041737895822118365078045556628444273925387517127854796781556346403714877681766899855392069265439424008711973674701749862626690747296762535803929376233833981046927874558605253696441650390625)$$

Mga Hakbang sa Paggamit ng Definition of Logarithm

I-divide ang magkabilang dulo ng equation gamit ang 75.

$$\frac{30}{75}=e^{-0.002t}$$

Bawasan ang fraction \frac{30}{75} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 15.

$$\frac{2}{5}=e^{-0.002t}$$

Pagpalitin ang magkabilang panig para nasa kaliwang bahagi ang lahat ng variable na term.

$$e^{-0.002t}=\frac{2}{5}$$

Kunin ang logarithm ng magkabilang dulo ng equation.

$$\log(e^{-0.002t})=\log(\frac{2}{5})$$

Ang logarithm ng isang numero na na-raise sa isang power ay ang power times ang logarithm ng numero.

$$-0.002t\log(e)=\log(\frac{2}{5})$$

I-divide ang magkabilang dulo ng equation gamit ang \log(e).

$$-0.002t=\frac{\log(\frac{2}{5})}{\log(e)}$$

Gamit ang change-of-base formula na \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$-0.002t=\log_{e}\left(\frac{2}{5}\right)$$

I-multiply ang magkabilang dulo ng equation gamit ang -500.

$$t=\frac{\ln(\frac{2}{5})}{-0.002}$$

I-solve ang t (complex solution)

$$t=-i\times 1000\pi n_{1}+\ln(9332636185032188789900895447238171696170914463717080246217143397959669109757756344544403270978811023595949899303242426242154875213540323948415208172039307562344106661383251502739950759859018315111004.90796265113118240512514795933790805178271125415103810698378854426481119469814228660959222017662910442798456169448887147466528006328368452647429261829862165202793195289493607117850663668741065439805530718136320599844826041954101213229629869502194514609904214608668361244792952034826864617657926916047420065936389041737895822118365078045556628444273925387517127854796781556346403714877681766899855392069265439424008711973674701749862626690747296762535803929376233833981046927874558605253696441650390625)$$

$$n_{1}\in \mathrm{Z}$$