Datrys 2=3^x+1

$$2= { 3 }^{ x+1 }$$

Datrys ar gyfer x

$$x=\log_{3}\left(2\right)-1\approx -0.369070246$$

Camau gan Ddefnyddio Diffiniad Logarithm

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

$$3^{x+1}=2$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{x+1})=\log(2)$$

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

$$\left(x+1\right)\log(3)=\log(2)$$

Rhannu’r ddwy ochr â \log(3).

$$x+1=\frac{\log(2)}{\log(3)}$$

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

$$x+1=\log_{3}\left(2\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$x=\log_{3}\left(2\right)-1$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(2\right)-1$$

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