Datrys 5*27^x=10.935

$$5 \times 27 ^ { x } = 10.935$$

Datrys ar gyfer x

$$x=-\log_{3}\left(10\right)+\frac{7}{3}\approx 0.237430059$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5\times 27^{x}=10.935$$

Rhannu’r ddwy ochr â 5.

$$27^{x}=2.187$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(27^{x})=\log(2.187)$$

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

$$x\log(27)=\log(2.187)$$

Rhannu’r ddwy ochr â \log(27).

$$x=\frac{\log(2.187)}{\log(27)}$$

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

$$x=\log_{27}\left(2.187\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(3)}-\log_{3}\left(10\right)+\frac{7}{3}$$

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