Datrys 100*5^x-4=0

$$100 \cdot 5 ^ { x } - 4 = 0$$

Datrys ar gyfer x

$$x=-2$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$100\times 5^{x}-4=0$$

Adio 4 at ddwy ochr yr hafaliad.

$$100\times 5^{x}=4$$

Rhannu’r ddwy ochr â 100.

$$5^{x}=\frac{1}{25}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{x})=\log(\frac{1}{25})$$

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

$$x\log(5)=\log(\frac{1}{25})$$

Rhannu’r ddwy ochr â \log(5).

$$x=\frac{\log(\frac{1}{25})}{\log(5)}$$

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

$$x=\log_{5}\left(\frac{1}{25}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}-2$$

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