Datrys e^frac{x{4}}=205

$$e ^ { \frac { x } { 4 } } = 205$$

Datrys ar gyfer x

$$x=4\ln(205)\approx 21.292039917$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{\frac{1}{4}x}=205$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{\frac{1}{4}x})=\log(205)$$

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

$$\frac{1}{4}x\log(e)=\log(205)$$

Rhannu’r ddwy ochr â \log(e).

$$\frac{1}{4}x=\frac{\log(205)}{\log(e)}$$

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

$$\frac{1}{4}x=\log_{e}\left(205\right)$$

Lluosi’r ddwy ochr â 4.

$$x=\frac{\ln(205)}{\frac{1}{4}}$$

Datrys ar gyfer x (complex solution)

$$x=4\ln(205)+i\times 8\pi n_{1}$$

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