Datrys 0.81^x=0.05

$${ 0.81 }^{ x } =0.05$$

Datrys ar gyfer x

$$x=-\frac{\log_{0.9}\left(20\right)}{2}\approx 14.216579403$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$0.81^{x}=0.05$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(0.81^{x})=\log(0.05)$$

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

$$x\log(0.81)=\log(0.05)$$

Rhannu’r ddwy ochr â \log(0.81).

$$x=\frac{\log(0.05)}{\log(0.81)}$$

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

$$x=\log_{0.81}\left(0.05\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(0.9)}-\frac{\log_{0.9}\left(20\right)}{2}$$

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