Datrys 7(1/3)^x=63

$$7 ( \frac { 1 } { 3 } ) ^ { x } = 63$$

Datrys ar gyfer x

$$x=-2$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$7\times \left(\frac{1}{3}\right)^{x}=63$$

Rhannu’r ddwy ochr â 7.

$$\left(\frac{1}{3}\right)^{x}=9$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{1}{3}\right)^{x})=\log(9)$$

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

$$x\log(\frac{1}{3})=\log(9)$$

Rhannu’r ddwy ochr â \log(\frac{1}{3}).

$$x=\frac{\log(9)}{\log(\frac{1}{3})}$$

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

$$x=\log_{\frac{1}{3}}\left(9\right)$$

Datrys ar gyfer x (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(3)}-2$$

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