Datrys 1.08^x=2

$$1.08 ^ { x } = 2$$

Datrys ar gyfer x

$$x=\log_{1.08}\left(2\right)\approx 9.006468342$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$1.08^{x}=2$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.08^{x})=\log(2)$$

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

$$x\log(1.08)=\log(2)$$

Rhannu’r ddwy ochr â \log(1.08).

$$x=\frac{\log(2)}{\log(1.08)}$$

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

$$x=\log_{1.08}\left(2\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.08)}+\log_{1.08}\left(2\right)$$

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