Datrys 12^x+3=15

$${ 12 }^{ x+3 } =15$$

Datrys ar gyfer x

$$x=-\log_{12}\left(\frac{576}{5}\right)\approx -1.910200429$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$12^{x+3}=15$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(12^{x+3})=\log(15)$$

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

$$\left(x+3\right)\log(12)=\log(15)$$

Rhannu’r ddwy ochr â \log(12).

$$x+3=\frac{\log(15)}{\log(12)}$$

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

$$x+3=\log_{12}\left(15\right)$$

Tynnu 3 o ddwy ochr yr hafaliad.

$$x=\log_{12}\left(15\right)-3$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(12)}-\log_{12}\left(\frac{576}{5}\right)$$

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