Datrys e^5n=1/2

$$e ^ { 5 n } = \frac { 1 } { 2 }$$

Datrys ar gyfer n

$$n=-\frac{\ln(2)}{5}\approx -0.138629436$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{5n}=\frac{1}{2}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{5n})=\log(\frac{1}{2})$$

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

$$5n\log(e)=\log(\frac{1}{2})$$

Rhannu’r ddwy ochr â \log(e).

$$5n=\frac{\log(\frac{1}{2})}{\log(e)}$$

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

$$5n=\log_{e}\left(\frac{1}{2}\right)$$

Rhannu’r ddwy ochr â 5.

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

Datrys ar gyfer n (complex solution)

$$n=\frac{i\times 2\pi n_{1}}{5}-\frac{\ln(2)}{5}$$

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