Datrys 12(2^x-5)=500

$$12 ( 2 ^ { x - 5 } ) = 500$$

Datrys ar gyfer x

$$x=\log_{2}\left(\frac{125}{3}\right)+5\approx 10.380821784$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$12\times 2^{x-5}=500$$

Rhannu’r ddwy ochr â 12.

$$2^{x-5}=\frac{125}{3}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{x-5})=\log(\frac{125}{3})$$

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

$$\left(x-5\right)\log(2)=\log(\frac{125}{3})$$

Rhannu’r ddwy ochr â \log(2).

$$x-5=\frac{\log(\frac{125}{3})}{\log(2)}$$

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

$$x-5=\log_{2}\left(\frac{125}{3}\right)$$

Adio 5 at ddwy ochr yr hafaliad.

$$x=\frac{\ln(\frac{125}{3})}{\ln(2)}-\left(-5\right)$$