Datrys 9000=3200(1.0775^x

$$9000=3200( { 1.0775 }^{ x }$$

Datrys ar gyfer x

$$x=\log_{1.0775}\left(2.8125\right)\approx 13.85349256$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 3200.

$$\frac{9000}{3200}=1.0775^{x}$$

Lleihau'r ffracsiwn \frac{9000}{3200} i'r graddau lleiaf posib drwy dynnu a chanslo allan 200.

$$\frac{45}{16}=1.0775^{x}$$

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

$$1.0775^{x}=\frac{45}{16}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.0775^{x})=\log(\frac{45}{16})$$

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

$$x\log(1.0775)=\log(\frac{45}{16})$$

Rhannu’r ddwy ochr â \log(1.0775).

$$x=\frac{\log(\frac{45}{16})}{\log(1.0775)}$$

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

$$x=\log_{1.0775}\left(\frac{45}{16}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.0775)}+\log_{1.0775}\left(2.8125\right)$$

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