Datrys 3^x+1=(27*3)^4

$$3 ^ { x + 1 } = ( 27 \cdot 3 ) ^ { 4 }$$

Datrys ar gyfer x

$$x=15$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{x+1}=43046721$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{x+1})=\log(43046721)$$

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

$$\left(x+1\right)\log(3)=\log(43046721)$$

Rhannu’r ddwy ochr â \log(3).

$$x+1=\frac{\log(43046721)}{\log(3)}$$

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

$$x+1=\log_{3}\left(43046721\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$x=16-1$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(3)}+15$$

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