Datrys 625=1/25*5^n-4

$$625 = \frac { 1 } { 25 } \times 5 ^ { n - 4 }$$

Datrys ar gyfer n

$$n=10$$

Camau gan Ddefnyddio Diffiniad Logarithm

Lluoswch y ddwy ochr â 25, cilyddol \frac{1}{25}.

$$625\times 25=5^{n-4}$$

Lluosi 625 a 25 i gael 15625.

$$15625=5^{n-4}$$

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

$$5^{n-4}=15625$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{n-4})=\log(15625)$$

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

$$\left(n-4\right)\log(5)=\log(15625)$$

Rhannu’r ddwy ochr â \log(5).

$$n-4=\frac{\log(15625)}{\log(5)}$$

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

$$n-4=\log_{5}\left(15625\right)$$

Adio 4 at ddwy ochr yr hafaliad.

$$n=6-\left(-4\right)$$

Datrys ar gyfer n (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(5)}+10$$

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