Datrys 3^n=2

$$3 ^ { n } = 2$$

Datrys ar gyfer n

$$n=\log_{3}\left(2\right)\approx 0.630929754$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{n}=2$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{n})=\log(2)$$

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

$$n\log(3)=\log(2)$$

Rhannu’r ddwy ochr â \log(3).

$$n=\frac{\log(2)}{\log(3)}$$

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

$$n=\log_{3}\left(2\right)$$

Datrys ar gyfer n (complex solution)

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

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