Datrys 1/9=243*({left(1/3right)}^x)

$$\frac{ 1 }{ 9 } =243 \times ( { \left( \frac{ 1 }{ 3 } \right) }^{ x } )$$

Datrys ar gyfer x

$$x=7$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 243.

$$\frac{\frac{1}{9}}{243}=\left(\frac{1}{3}\right)^{x}$$

Mynegwch \frac{\frac{1}{9}}{243} fel ffracsiwn unigol.

$$\frac{1}{9\times 243}=\left(\frac{1}{3}\right)^{x}$$

Lluosi 9 a 243 i gael 2187.

$$\frac{1}{2187}=\left(\frac{1}{3}\right)^{x}$$

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

$$\left(\frac{1}{3}\right)^{x}=\frac{1}{2187}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{1}{3}\right)^{x})=\log(\frac{1}{2187})$$

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

$$x\log(\frac{1}{3})=\log(\frac{1}{2187})$$

Rhannu’r ddwy ochr â \log(\frac{1}{3}).

$$x=\frac{\log(\frac{1}{2187})}{\log(\frac{1}{3})}$$

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

$$x=\log_{\frac{1}{3}}\left(\frac{1}{2187}\right)$$

Datrys ar gyfer x (complex solution)

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

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