Datrys 103^x=2

$$103 ^ { x } = 2$$

Datrys ar gyfer x

$$x=\log_{103}\left(2\right)\approx 0.149555062$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$103^{x}=2$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(103^{x})=\log(2)$$

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

$$x\log(103)=\log(2)$$

Rhannu’r ddwy ochr â \log(103).

$$x=\frac{\log(2)}{\log(103)}$$

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

$$x=\log_{103}\left(2\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(103)}+\log_{103}\left(2\right)$$

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