Datrys 32^x+3=2

$$32 ^ { x + 3 } = 2$$

Datrys ar gyfer x

$$x = -\frac{14}{5} = -2\frac{4}{5} = -2.8$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$32^{x+3}=2$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(32^{x+3})=\log(2)$$

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

$$\left(x+3\right)\log(32)=\log(2)$$

Rhannu’r ddwy ochr â \log(32).

$$x+3=\frac{\log(2)}{\log(32)}$$

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

$$x+3=\log_{32}\left(2\right)$$

Tynnu 3 o ddwy ochr yr hafaliad.

$$x=\frac{1}{5}-3$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{5\ln(2)}-\frac{14}{5}$$

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