Datrys 3^x-2*3^x*3^-2=7

$${ 3 }^{ x } -2 \times { 3 }^{ x } \times { 3 }^{ -2 } =7$$

Datrys ar gyfer x

$$x=2$$

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfrifo 3 i bŵer -2 a chael \frac{1}{9}.

$$3^{x}-2\times 3^{x}\times \frac{1}{9}=7$$

Lluosi 2 a \frac{1}{9} i gael \frac{2}{9}.

$$3^{x}-\frac{2}{9}\times 3^{x}=7$$

Cyfuno 3^{x} a -\frac{2}{9}\times 3^{x} i gael \frac{7}{9}\times 3^{x}.

$$\frac{7}{9}\times 3^{x}=7$$

Lluoswch y ddwy ochr â \frac{9}{7}, cilyddol \frac{7}{9}.

$$3^{x}=7\times \frac{9}{7}$$

Lluosi 7 a \frac{9}{7} i gael 9.

$$3^{x}=9$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{x})=\log(9)$$

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

$$x\log(3)=\log(9)$$

Rhannu’r ddwy ochr â \log(3).

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

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

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

Datrys ar gyfer x (complex solution)

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

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