Datrys (2/7)^-3*(2/7)^-11=(2/7)^x

$$( \frac { 2 } { 7 } ) ^ { - 3 } \times ( \frac { 2 } { 7 } ) ^ { - 11 } = ( \frac { 2 } { 7 } ) ^ { x }$$

Datrys ar gyfer x

$$x=-14$$

Camau gan Ddefnyddio Diffiniad Logarithm

Er mwyn lluosi pwerau sy’n rhannu’r un sail, adiwch eu esbonyddion. Adiwch -3 a -11 i gael -14.

$$\left(\frac{2}{7}\right)^{-14}=\left(\frac{2}{7}\right)^{x}$$

Cyfrifo \frac{2}{7} i bŵer -14 a chael \frac{678223072849}{16384}.

$$\frac{678223072849}{16384}=\left(\frac{2}{7}\right)^{x}$$

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$\left(\frac{2}{7}\right)^{x}=\frac{678223072849}{16384}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{2}{7}\right)^{x})=\log(\frac{678223072849}{16384})$$

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

$$x\log(\frac{2}{7})=\log(\frac{678223072849}{16384})$$

Rhannu’r ddwy ochr â \log(\frac{2}{7}).

$$x=\frac{\log(\frac{678223072849}{16384})}{\log(\frac{2}{7})}$$

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

$$x=\log_{\frac{2}{7}}\left(\frac{678223072849}{16384}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{2}{7})}+2\log_{\frac{2}{7}}\left(\frac{823543}{128}\right)$$

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