Datrys e^0.48x=11

$$e ^ { 0.48 x } = 11$$

Datrys ar gyfer x

$$x=\frac{25\ln(11)}{12}\approx 4.995615152$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{0.48x}=11$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{0.48x})=\log(11)$$

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

$$0.48x\log(e)=\log(11)$$

Rhannu’r ddwy ochr â \log(e).

$$0.48x=\frac{\log(11)}{\log(e)}$$

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

$$0.48x=\log_{e}\left(11\right)$$

Rhannu dwy ochr hafaliad â 0.48, sydd yr un peth â lluosi’r ddwy ochr â chilydd y ffracsiwn.

$$x=\frac{\ln(11)}{0.48}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 25\pi n_{1}}{6}+\frac{25\ln(11)}{12}$$

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