Datrys 9^x-1=27

$$9 ^ { x - 1 } = 27$$

Datrys ar gyfer x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$9^{x-1}=27$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(9^{x-1})=\log(27)$$

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

$$\left(x-1\right)\log(9)=\log(27)$$

Rhannu’r ddwy ochr â \log(9).

$$x-1=\frac{\log(27)}{\log(9)}$$

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

$$x-1=\log_{9}\left(27\right)$$

Adio 1 at ddwy ochr yr hafaliad.

$$x=\frac{3}{2}-\left(-1\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(3)}+\frac{5}{2}$$

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