Datrys 19=7+17e^-0.034t

$$19 = 7 + 17 e ^ { - 0.034 t }$$

Datrys ar gyfer t

$$t=\frac{500\ln(17)-500\ln(12)}{17}\approx 10.244314537$$

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$7+17e^{-0.034t}=19$$

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$17e^{-0.034t}+7=19$$

Tynnu 7 o ddwy ochr yr hafaliad.

$$17e^{-0.034t}=12$$

Rhannu’r ddwy ochr â 17.

$$e^{-0.034t}=\frac{12}{17}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{-0.034t})=\log(\frac{12}{17})$$

Logarithm rhif wedi’i godi i bŵer yw’r pŵer wedi’i lluosi â logarithm y rhif.

$$-0.034t\log(e)=\log(\frac{12}{17})$$

Rhannu’r ddwy ochr â \log(e).

$$-0.034t=\frac{\log(\frac{12}{17})}{\log(e)}$$

Gyda’r fformiwla newid-sail \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$-0.034t=\log_{e}\left(\frac{12}{17}\right)$$

Rhannu dwy ochr hafaliad â -0.034, sydd yr un peth â lluosi’r ddwy ochr â chilydd y ffracsiwn.

$$t=\frac{\ln(\frac{12}{17})}{-0.034}$$

Datrys ar gyfer t (complex solution)

$$t=-\frac{i\times 1000\pi n_{1}}{17}+\frac{500\ln(17)}{17}-\frac{500\ln(12)}{17}$$

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