Datrys 5^-x=4

$$5 ^ { - x } = 4$$

Datrys ar gyfer x

$$x=-2\log_{5}\left(2\right)\approx -0.861353116$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5^{-x}=4$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{-x})=\log(4)$$

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

$$-x\log(5)=\log(4)$$

Rhannu’r ddwy ochr â \log(5).

$$-x=\frac{\log(4)}{\log(5)}$$

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

$$-x=\log_{5}\left(4\right)$$

Rhannu’r ddwy ochr â -1.

$$x=\frac{2\log_{5}\left(2\right)}{-1}$$

Datrys ar gyfer x (complex solution)

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

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