Datrys 11*13^x-14=106

$$11 \times { 13 }^{ x } -14=106$$

Datrys ar gyfer x

$$x=\log_{13}\left(\frac{120}{11}\right)\approx 0.931634951$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$11\times 13^{x}-14=106$$

Adio 14 at ddwy ochr yr hafaliad.

$$11\times 13^{x}=120$$

Rhannu’r ddwy ochr â 11.

$$13^{x}=\frac{120}{11}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(13^{x})=\log(\frac{120}{11})$$

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

$$x\log(13)=\log(\frac{120}{11})$$

Rhannu’r ddwy ochr â \log(13).

$$x=\frac{\log(\frac{120}{11})}{\log(13)}$$

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

$$x=\log_{13}\left(\frac{120}{11}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(13)}+\log_{13}\left(\frac{120}{11}\right)$$

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