Datrys 10(107)^x=2000

$$10 ( 107 ) ^ { x } = 2000$$

Datrys ar gyfer x

$$x=\log_{107}\left(200\right)\approx 1.133856504$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$10\times 107^{x}=2000$$

Rhannu’r ddwy ochr â 10.

$$107^{x}=200$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(107^{x})=\log(200)$$

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

$$x\log(107)=\log(200)$$

Rhannu’r ddwy ochr â \log(107).

$$x=\frac{\log(200)}{\log(107)}$$

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

$$x=\log_{107}\left(200\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(107)}+\log_{107}\left(200\right)$$

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