Datrys e^-9y=11

$$e ^ { - 9 y } = 11$$

Datrys ar gyfer y

$$y=-\frac{\ln(11)}{9}\approx -0.266432808$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{-9y}=11$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{-9y})=\log(11)$$

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

$$-9y\log(e)=\log(11)$$

Rhannu’r ddwy ochr â \log(e).

$$-9y=\frac{\log(11)}{\log(e)}$$

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

$$-9y=\log_{e}\left(11\right)$$

Rhannu’r ddwy ochr â -9.

$$y=\frac{\ln(11)}{-9}$$

Datrys ar gyfer y (complex solution)

$$y=-\frac{i\times 2\pi n_{1}}{9}-\frac{\ln(11)}{9}$$

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