Datrys 25^n=100

$$25 ^ { n } = 100$$

Datrys ar gyfer n

$$n=\log_{5}\left(10\right)\approx 1.430676558$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$25^{n}=100$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(25^{n})=\log(100)$$

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

$$n\log(25)=\log(100)$$

Rhannu’r ddwy ochr â \log(25).

$$n=\frac{\log(100)}{\log(25)}$$

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

$$n=\log_{25}\left(100\right)$$

Datrys ar gyfer n (complex solution)

$$n=\frac{\pi n_{1}i}{\ln(5)}+\log_{5}\left(10\right)$$

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