Datrys 128^x=5000

$$128 ^ { x } = 5000$$

Datrys ar gyfer x

$$x = \frac{\log_{2} {(5000)}}{7} \approx 1.755387483$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$128^{x}=5000$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(128^{x})=\log(5000)$$

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

$$x\log(128)=\log(5000)$$

Rhannu’r ddwy ochr â \log(128).

$$x=\frac{\log(5000)}{\log(128)}$$

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

$$x=\log_{128}\left(5000\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{7\ln(2)}+\frac{\log_{2}\left(5000\right)}{7}$$

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