Datrys 2097=5954.3{(e)^x*(-0.00896)}

$$2097=5954.3 {(e)^{ x \times (-0.00896) }}$$

Datrys ar gyfer x

$$x=\frac{3125\ln(59543)-3125\ln(20970)}{28}\approx 116.473872288$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 5954.3.

$$\frac{2097}{5954.3}=e^{x\left(-0.00896\right)}$$

Ehangu \frac{2097}{5954.3} drwy luosi'r rhifiadur a'r enwadur gyda 10.

$$\frac{20970}{59543}=e^{x\left(-0.00896\right)}$$

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

$$e^{x\left(-0.00896\right)}=\frac{20970}{59543}$$

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{-0.00896x}=\frac{20970}{59543}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{-0.00896x})=\log(\frac{20970}{59543})$$

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

$$-0.00896x\log(e)=\log(\frac{20970}{59543})$$

Rhannu’r ddwy ochr â \log(e).

$$-0.00896x=\frac{\log(\frac{20970}{59543})}{\log(e)}$$

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

$$-0.00896x=\log_{e}\left(\frac{20970}{59543}\right)$$

Rhannu dwy ochr hafaliad â -0.00896, sydd yr un peth â lluosi’r ddwy ochr â chilydd y ffracsiwn.

$$x=\frac{\ln(\frac{20970}{59543})}{-0.00896}$$

Datrys ar gyfer x (complex solution)

$$x=-\frac{i\times 3125\pi n_{1}}{14}+\frac{3125\ln(59543)}{28}-\frac{3125\ln(20970)}{28}$$

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