Datrys f(x)=200*1.16^x=1000

$$f ( x ) = 200 \cdot 1.16 ^ { x } = 1000$$

Datrys ar gyfer x

$$x=\log_{1.16}\left(5\right)\approx 10.843807148$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$200\times 1.16^{x}=1000$$

Rhannu’r ddwy ochr â 200.

$$1.16^{x}=5$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.16^{x})=\log(5)$$

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

$$x\log(1.16)=\log(5)$$

Rhannu’r ddwy ochr â \log(1.16).

$$x=\frac{\log(5)}{\log(1.16)}$$

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

$$x=\log_{1.16}\left(5\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.16)}+\log_{1.16}\left(5\right)$$

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