Datrys f(x)=200*116^x=1000

$$f ( x ) = 200 \cdot 116 ^ { x } = 1000$$

Datrys ar gyfer x

$$x=\log_{116}\left(5\right)\approx 0.338573131$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$200\times 116^{x}=1000$$

Rhannu’r ddwy ochr â 200.

$$116^{x}=5$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(116^{x})=\log(5)$$

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

$$x\log(116)=\log(5)$$

Rhannu’r ddwy ochr â \log(116).

$$x=\frac{\log(5)}{\log(116)}$$

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

$$x=\log_{116}\left(5\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(116)}+\log_{116}\left(5\right)$$

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