Datrys 3^n=4

$$3 ^ { n } = 4$$

Datrys ar gyfer n

$$n=2\log_{3}\left(2\right)\approx 1.261859507$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{n}=4$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{n})=\log(4)$$

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

$$n\log(3)=\log(4)$$

Rhannu’r ddwy ochr â \log(3).

$$n=\frac{\log(4)}{\log(3)}$$

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

$$n=\log_{3}\left(4\right)$$

Datrys ar gyfer n (complex solution)

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

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