Datrys 9^x+2=6

$$9 ^ { x + 2 } = 6$$

Datrys ar gyfer x

$$x=\frac{\log_{3}\left(6\right)-4}{2}\approx -1.184535123$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$9^{x+2}=6$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(9^{x+2})=\log(6)$$

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

$$\left(x+2\right)\log(9)=\log(6)$$

Rhannu’r ddwy ochr â \log(9).

$$x+2=\frac{\log(6)}{\log(9)}$$

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

$$x+2=\log_{9}\left(6\right)$$

Tynnu 2 o ddwy ochr yr hafaliad.

$$x=\frac{\log_{3}\left(6\right)}{2}-2$$

Datrys ar gyfer x (complex solution)

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

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