Datrys 5^x-8-4=52

$$5 ^ { x - 8 } - 4 = 52$$

Datrys ar gyfer x

$$x=\log_{5}\left(56\right)+8\approx 10.501091629$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5^{x-8}-4=52$$

Adio 4 at ddwy ochr yr hafaliad.

$$5^{x-8}=56$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{x-8})=\log(56)$$

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

$$\left(x-8\right)\log(5)=\log(56)$$

Rhannu’r ddwy ochr â \log(5).

$$x-8=\frac{\log(56)}{\log(5)}$$

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

$$x-8=\log_{5}\left(56\right)$$

Adio 8 at ddwy ochr yr hafaliad.

$$x=\log_{5}\left(56\right)-\left(-8\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(5)}+\log_{5}\left(56\right)+8$$

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