Datrys 4599*1.25^x=10000

$$4599 \times { 1.25 }^{ x } =10000$$

Datrys ar gyfer x

$$x=\log_{1.25}\left(\frac{10000}{4599}\right)\approx 3.480926067$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$4599\times 1.25^{x}=10000$$

Rhannu’r ddwy ochr â 4599.

$$1.25^{x}=\frac{10000}{4599}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.25^{x})=\log(\frac{10000}{4599})$$

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

$$x\log(1.25)=\log(\frac{10000}{4599})$$

Rhannu’r ddwy ochr â \log(1.25).

$$x=\frac{\log(\frac{10000}{4599})}{\log(1.25)}$$

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

$$x=\log_{1.25}\left(\frac{10000}{4599}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.25)}+\log_{1.25}\left(\frac{10000}{4599}\right)$$

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