Datrys 11^x=5

$$11 ^ { x } = 5$$

Datrys ar gyfer x

$$x=\log_{11}\left(5\right)\approx 0.671187741$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$11^{x}=5$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(11^{x})=\log(5)$$

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

$$x\log(11)=\log(5)$$

Rhannu’r ddwy ochr â \log(11).

$$x=\frac{\log(5)}{\log(11)}$$

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

$$x=\log_{11}\left(5\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(11)}+\log_{11}\left(5\right)$$

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