Datrys 180434=10225^4x

$$180434= { 10225 }^{ 4x }$$

Datrys ar gyfer x

$$x=\frac{\log_{10225}\left(180434\right)}{4}\approx 0.327728163$$

Camau gan Ddefnyddio Diffiniad Logarithm

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

$$10225^{4x}=180434$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(10225^{4x})=\log(180434)$$

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

$$4x\log(10225)=\log(180434)$$

Rhannu’r ddwy ochr â \log(10225).

$$4x=\frac{\log(180434)}{\log(10225)}$$

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

$$4x=\log_{10225}\left(180434\right)$$

Rhannu’r ddwy ochr â 4.

$$x=\frac{\log_{10225}\left(180434\right)}{4}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{2\ln(10225)}+\frac{\log_{10225}\left(180434\right)}{4}$$

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