Datrys 3^x+2=3^5

$$3 ^ { x + 2 } = 3 ^ { 5 }$$

Datrys ar gyfer x

$$x=3$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{x+2}=243$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{x+2})=\log(243)$$

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

$$\left(x+2\right)\log(3)=\log(243)$$

Rhannu’r ddwy ochr â \log(3).

$$x+2=\frac{\log(243)}{\log(3)}$$

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

$$x+2=\log_{3}\left(243\right)$$

Tynnu 2 o ddwy ochr yr hafaliad.

$$x=5-2$$

Datrys ar gyfer x (complex solution)

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

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