Datrys 61=3490(0.915)^x-2-109

$$61 = 3490 ( 0.915 ) ^ { x - 2 } - 109$$

Datrys ar gyfer x

$$x=-\log_{0.915}\left(\frac{13960000}{569313}\right)\approx 36.017981429$$

Camau gan Ddefnyddio Diffiniad Logarithm

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

$$3490\times 0.915^{x-2}-109=61$$

Adio 109 at ddwy ochr yr hafaliad.

$$3490\times 0.915^{x-2}=170$$

Rhannu’r ddwy ochr â 3490.

$$0.915^{x-2}=\frac{17}{349}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(0.915^{x-2})=\log(\frac{17}{349})$$

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

$$\left(x-2\right)\log(0.915)=\log(\frac{17}{349})$$

Rhannu’r ddwy ochr â \log(0.915).

$$x-2=\frac{\log(\frac{17}{349})}{\log(0.915)}$$

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

$$x-2=\log_{0.915}\left(\frac{17}{349}\right)$$

Adio 2 at ddwy ochr yr hafaliad.

$$x=\frac{\ln(\frac{17}{349})}{\ln(\frac{183}{200})}-\left(-2\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(0.915)}-\log_{0.915}\left(\frac{13960000}{569313}\right)$$

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