Datrys 243=9^2x+1

$$243 = 9 ^ { 2 x + 1 }$$

Datrys ar gyfer x

$$x=\frac{3}{4}=0.75$$

Camau gan Ddefnyddio Diffiniad Logarithm

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

$$9^{2x+1}=243$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(9^{2x+1})=\log(243)$$

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

$$\left(2x+1\right)\log(9)=\log(243)$$

Rhannu’r ddwy ochr â \log(9).

$$2x+1=\frac{\log(243)}{\log(9)}$$

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

$$2x+1=\log_{9}\left(243\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$2x=\frac{5}{2}-1$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\frac{3}{2}}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\pi n_{1}}{2\ln(3)}+\frac{3}{4}$$

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