Datrys 2^x+2^x=2^18

$${ 2 }^{ x } + { 2 }^{ x } = { 2 }^{ 18 }$$

Datrys ar gyfer x

$$x=17$$

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfuno 2^{x} a 2^{x} i gael 2\times 2^{x}.

$$2\times 2^{x}=2^{18}$$

Cyfrifo 2 i bŵer 18 a chael 262144.

$$2\times 2^{x}=262144$$

Rhannu’r ddwy ochr â 2.

$$2^{x}=\frac{262144}{2}$$

Rhannu 262144 â 2 i gael 131072.

$$2^{x}=131072$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{x})=\log(131072)$$

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

$$x\log(2)=\log(131072)$$

Rhannu’r ddwy ochr â \log(2).

$$x=\frac{\log(131072)}{\log(2)}$$

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

$$x=\log_{2}\left(131072\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+17$$

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