Datrys (2^3x-1+10)div7=6

$$( 2 ^ { 3 x - 1 } + 10 ) \div 7 = 6$$

Datrys ar gyfer x

$$x=2$$

Camau gan Ddefnyddio Diffiniad Logarithm

Lluosi’r ddwy ochr â 7.

$$2^{3x-1}+10=6\times 7$$

Lluosi 6 a 7 i gael 42.

$$2^{3x-1}+10=42$$

Tynnu 10 o ddwy ochr yr hafaliad.

$$2^{3x-1}=32$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{3x-1})=\log(32)$$

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

$$\left(3x-1\right)\log(2)=\log(32)$$

Rhannu’r ddwy ochr â \log(2).

$$3x-1=\frac{\log(32)}{\log(2)}$$

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

$$3x-1=\log_{2}\left(32\right)$$

Adio 1 at ddwy ochr yr hafaliad.

$$3x=5-\left(-1\right)$$

Rhannu’r ddwy ochr â 3.

$$x=\frac{6}{3}$$

Datrys ar gyfer x (complex solution)

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

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