Datrys 47=610(0.5)^frac{x{4}}

$$47 = 610 ( 0.5 ) ^ { \frac { x } { 4 } }$$

Datrys ar gyfer x

$$x=4\log_{2}\left(\frac{610}{47}\right)\approx 14.792306323$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 610.

$$\frac{47}{610}=0.5^{\frac{x}{4}}$$

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$0.5^{\frac{x}{4}}=\frac{47}{610}$$

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$0.5^{\frac{1}{4}x}=\frac{47}{610}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(0.5^{\frac{1}{4}x})=\log(\frac{47}{610})$$

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

$$\frac{1}{4}x\log(0.5)=\log(\frac{47}{610})$$

Rhannu’r ddwy ochr â \log(0.5).

$$\frac{1}{4}x=\frac{\log(\frac{47}{610})}{\log(0.5)}$$

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

$$\frac{1}{4}x=\log_{0.5}\left(\frac{47}{610}\right)$$

Lluosi’r ddwy ochr â 4.

$$x=-\frac{\frac{\ln(\frac{47}{610})}{\ln(2)}}{\frac{1}{4}}$$

Datrys ar gyfer x (complex solution)

$$x=-\frac{i\times 8\pi n_{1}}{\ln(2)}+4\log_{2}\left(\frac{610}{47}\right)$$

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