Datrys 2^4=8^x

$$2 ^ { 4 } = 8 ^ { x }$$

Datrys ar gyfer x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfrifo 2 i bŵer 4 a chael 16.

$$16=8^{x}$$

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

$$8^{x}=16$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(8^{x})=\log(16)$$

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

$$x\log(8)=\log(16)$$

Rhannu’r ddwy ochr â \log(8).

$$x=\frac{\log(16)}{\log(8)}$$

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

$$x=\log_{8}\left(16\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(2)}+\frac{4}{3}$$

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