Datrys -6*2^0.1x=-100

$$- 6 \cdot 2 ^ { 0.1 x } = - 100$$

Datrys ar gyfer x

$$x=\log_{2}\left(\frac{95367431640625}{59049}\right)+10\approx 40.588936891$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â -6.

$$2^{0.1x}=\frac{-100}{-6}$$

Lleihau'r ffracsiwn \frac{-100}{-6} i'r graddau lleiaf posib drwy dynnu a chanslo allan -2.

$$2^{0.1x}=\frac{50}{3}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{0.1x})=\log(\frac{50}{3})$$

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

$$0.1x\log(2)=\log(\frac{50}{3})$$

Rhannu’r ddwy ochr â \log(2).

$$0.1x=\frac{\log(\frac{50}{3})}{\log(2)}$$

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

$$0.1x=\log_{2}\left(\frac{50}{3}\right)$$

Lluosi’r ddwy ochr â 10.

$$x=\frac{\ln(\frac{50}{3})}{0.1\ln(2)}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 20\pi n_{1}}{\ln(2)}+\log_{2}\left(\frac{95367431640625}{59049}\right)+10$$

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