Datrys 3*2^frac{x{5}}=150

$$3 \cdot 2 ^ { \frac { x } { 5 } } = 150$$

Datrys ar gyfer x

$$x=10\log_{2}\left(5\right)+5\approx 28.219280949$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3\times 2^{\frac{1}{5}x}=150$$

Rhannu’r ddwy ochr â 3.

$$2^{\frac{1}{5}x}=50$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{\frac{1}{5}x})=\log(50)$$

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

$$\frac{1}{5}x\log(2)=\log(50)$$

Rhannu’r ddwy ochr â \log(2).

$$\frac{1}{5}x=\frac{\log(50)}{\log(2)}$$

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

$$\frac{1}{5}x=\log_{2}\left(50\right)$$

Lluosi’r ddwy ochr â 5.

$$x=\frac{\log_{2}\left(50\right)}{\frac{1}{5}}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{10\pi n_{1}i}{\ln(2)}+10\log_{2}\left(5\right)+5$$

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