Datrys 14400=4000(1025)^x

$$14400 = 4000 ( 1025 ) ^ { x }$$

Datrys ar gyfer x

$$x=\log_{1025}\left(\frac{18}{5}\right)\approx 0.184773671$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 4000.

$$\frac{14400}{4000}=1025^{x}$$

Lleihau'r ffracsiwn \frac{14400}{4000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 800.

$$\frac{18}{5}=1025^{x}$$

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

$$1025^{x}=\frac{18}{5}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1025^{x})=\log(\frac{18}{5})$$

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

$$x\log(1025)=\log(\frac{18}{5})$$

Rhannu’r ddwy ochr â \log(1025).

$$x=\frac{\log(\frac{18}{5})}{\log(1025)}$$

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

$$x=\log_{1025}\left(\frac{18}{5}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1025)}+\log_{1025}\left(\frac{18}{5}\right)$$

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