Datrys 3800=123^x

$$3800 = 123 ^ { x }$$

Datrys ar gyfer x

$$x=\log_{123}\left(3800\right)\approx 1.712892885$$

Camau gan Ddefnyddio Diffiniad Logarithm

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

$$123^{x}=3800$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(123^{x})=\log(3800)$$

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

$$x\log(123)=\log(3800)$$

Rhannu’r ddwy ochr â \log(123).

$$x=\frac{\log(3800)}{\log(123)}$$

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

$$x=\log_{123}\left(3800\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(123)}+\log_{123}\left(3800\right)$$

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