Datrys 6*2^frac{x{4}}=222

$$6 \cdot 2 ^ { \frac { x } { 4 } } = 222$$

Datrys ar gyfer x

$$x=4\log_{2}\left(37\right)\approx 20.837813463$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$6\times 2^{\frac{1}{4}x}=222$$

Rhannu’r ddwy ochr â 6.

$$2^{\frac{1}{4}x}=37$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{\frac{1}{4}x})=\log(37)$$

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

$$\frac{1}{4}x\log(2)=\log(37)$$

Rhannu’r ddwy ochr â \log(2).

$$\frac{1}{4}x=\frac{\log(37)}{\log(2)}$$

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

$$\frac{1}{4}x=\log_{2}\left(37\right)$$

Lluosi’r ddwy ochr â 4.

$$x=\frac{\log_{2}\left(37\right)}{\frac{1}{4}}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{8\pi n_{1}i}{\ln(2)}+4\log_{2}\left(37\right)$$

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