Datrys 2^x+1+2^x+1=20

$${ 2 }^{ x+1 } + { 2 }^{ x+1 } = 20$$

Datrys ar gyfer x

$$x=\log_{2}\left(5\right)\approx 2.321928095$$

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfuno 2^{x+1} a 2^{x+1} i gael 2\times 2^{x+1}.

$$2\times 2^{x+1}=20$$

Rhannu’r ddwy ochr â 2.

$$2^{x+1}=\frac{20}{2}$$

Rhannu 20 â 2 i gael 10.

$$2^{x+1}=10$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{x+1})=\log(10)$$

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

$$\left(x+1\right)\log(2)=\log(10)$$

Rhannu’r ddwy ochr â \log(2).

$$x+1=\frac{\log(10)}{\log(2)}$$

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

$$x+1=\log_{2}\left(10\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$x=\log_{2}\left(10\right)-1$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+\log_{2}\left(5\right)$$

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