Datrys 3000*1.032^x=6000

$$3000 \times { 1.032 }^{ x } =6000$$

Datrys ar gyfer x

$$x=\log_{1.032}\left(2\right)\approx 22.005603579$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3000\times 1.032^{x}=6000$$

Rhannu’r ddwy ochr â 3000.

$$1.032^{x}=2$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.032^{x})=\log(2)$$

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

$$x\log(1.032)=\log(2)$$

Rhannu’r ddwy ochr â \log(1.032).

$$x=\frac{\log(2)}{\log(1.032)}$$

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

$$x=\log_{1.032}\left(2\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.032)}+\log_{1.032}\left(2\right)$$

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