Datrys -486=-6^x-1

$$- 486 = - 6 ^ { x - 1 }$$

Datrys ar gyfer x

$$x=2\log_{6}\left(54\right)\approx 4.452588771$$

Camau gan Ddefnyddio Diffiniad Logarithm

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

$$-6^{x-1}=-486$$

Rhannu’r ddwy ochr â -1.

$$6^{x-1}=\frac{-486}{-1}$$

Gellir symlhau’r ffracsiwn \frac{-486}{-1} i 486 drwy dynnu’r arwydd negatif o’r rhifiadur a’r enwadur.

$$6^{x-1}=486$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(6^{x-1})=\log(486)$$

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

$$\left(x-1\right)\log(6)=\log(486)$$

Rhannu’r ddwy ochr â \log(6).

$$x-1=\frac{\log(486)}{\log(6)}$$

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

$$x-1=\log_{6}\left(486\right)$$

Adio 1 at ddwy ochr yr hafaliad.

$$x=\log_{6}\left(486\right)-\left(-1\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(6)}+2\log_{6}\left(54\right)$$

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