Datrys 5000=1,042^x

$$5000 = 1,042 ^ { x }$$

Datrys ar gyfer x

$$x=\log_{1042}\left(5000\right)\approx 1.225689907$$

Camau gan Ddefnyddio Diffiniad Logarithm

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

$$1042^{x}=5000$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1042^{x})=\log(5000)$$

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

$$x\log(1042)=\log(5000)$$

Rhannu’r ddwy ochr â \log(1042).

$$x=\frac{\log(5000)}{\log(1042)}$$

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

$$x=\log_{1042}\left(5000\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1042)}+\log_{1042}\left(5000\right)$$

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