Datrys 12(25)^x-1=75

$$12 ( 25 ) ^ { x - 1 } = 75$$

Datrys ar gyfer x

$$x=-\log_{5}\left(2\right)+2\approx 1.569323442$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$12\times 25^{x-1}=75$$

Rhannu’r ddwy ochr â 12.

$$25^{x-1}=\frac{25}{4}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(25^{x-1})=\log(\frac{25}{4})$$

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

$$\left(x-1\right)\log(25)=\log(\frac{25}{4})$$

Rhannu’r ddwy ochr â \log(25).

$$x-1=\frac{\log(\frac{25}{4})}{\log(25)}$$

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

$$x-1=\log_{25}\left(\frac{25}{4}\right)$$

Adio 1 at ddwy ochr yr hafaliad.

$$x=-\log_{5}\left(2\right)+1-\left(-1\right)$$

Datrys ar gyfer x (complex solution)

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

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