Datrys 3^-1x-1=1/9

$$3 ^ { - 1 x - 1 } = \frac { 1 } { 9 }$$

Datrys ar gyfer x

$$x=1$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{-x-1}=\frac{1}{9}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{-x-1})=\log(\frac{1}{9})$$

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

$$\left(-x-1\right)\log(3)=\log(\frac{1}{9})$$

Rhannu’r ddwy ochr â \log(3).

$$-x-1=\frac{\log(\frac{1}{9})}{\log(3)}$$

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

$$-x-1=\log_{3}\left(\frac{1}{9}\right)$$

Adio 1 at ddwy ochr yr hafaliad.

$$-x=-2-\left(-1\right)$$

Rhannu’r ddwy ochr â -1.

$$x=-\frac{1}{-1}$$

Datrys ar gyfer x (complex solution)

$$x=-\frac{i\times 2\pi n_{1}}{\ln(3)}+1$$

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