Datrys 27^2x=98

$$27 ^ { 2 x } = 98$$

Datrys ar gyfer x

$$x=\frac{\log_{3}\left(98\right)}{6}\approx 0.695569542$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$27^{2x}=98$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(27^{2x})=\log(98)$$

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

$$2x\log(27)=\log(98)$$

Rhannu’r ddwy ochr â \log(27).

$$2x=\frac{\log(98)}{\log(27)}$$

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

$$2x=\log_{27}\left(98\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\log_{3}\left(98\right)}{2\times 3}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{3\ln(3)}+\frac{\log_{3}\left(98\right)}{6}$$

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