Datrys 94*2^frac{x{3}}=16

$$94 \cdot 2 ^ { \frac { x } { 3 } } = 16$$

Datrys ar gyfer x

$$x=-3\log_{2}\left(47\right)+9\approx -7.663766555$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$94\times 2^{\frac{1}{3}x}=16$$

Rhannu’r ddwy ochr â 94.

$$2^{\frac{1}{3}x}=\frac{8}{47}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{\frac{1}{3}x})=\log(\frac{8}{47})$$

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

$$\frac{1}{3}x\log(2)=\log(\frac{8}{47})$$

Rhannu’r ddwy ochr â \log(2).

$$\frac{1}{3}x=\frac{\log(\frac{8}{47})}{\log(2)}$$

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

$$\frac{1}{3}x=\log_{2}\left(\frac{8}{47}\right)$$

Lluosi’r ddwy ochr â 3.

$$x=\frac{-\log_{2}\left(47\right)+3}{\frac{1}{3}}$$