Datrys 20^x=2020

$$20 ^ { x } = 2020$$

Datrys ar gyfer x

$$x=\log_{20}\left(2020\right)\approx 2.540565076$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$20^{x}=2020$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(20^{x})=\log(2020)$$

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

$$x\log(20)=\log(2020)$$

Rhannu’r ddwy ochr â \log(20).

$$x=\frac{\log(2020)}{\log(20)}$$

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

$$x=\log_{20}\left(2020\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(20)}+\log_{20}\left(2020\right)$$

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