Datrys 3^7=3^3x

$$3 ^ { 7 } = 3 ^ { 3 x }$$

Datrys ar gyfer x

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfrifo 3 i bŵer 7 a chael 2187.

$$2187=3^{3x}$$

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

$$3^{3x}=2187$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{3x})=\log(2187)$$

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

$$3x\log(3)=\log(2187)$$

Rhannu’r ddwy ochr â \log(3).

$$3x=\frac{\log(2187)}{\log(3)}$$

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

$$3x=\log_{3}\left(2187\right)$$

Rhannu’r ddwy ochr â 3.

$$x=\frac{7}{3}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(3)}+\frac{7}{3}$$

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