Datrys 7=8^x+1

$$7 = 8 ^ { x + 1 }$$

Datrys ar gyfer x

$$x=\frac{\log_{2}\left(7\right)-3}{3}\approx -0.064215026$$

Camau gan Ddefnyddio Diffiniad Logarithm

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

$$8^{x+1}=7$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(8^{x+1})=\log(7)$$

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

$$\left(x+1\right)\log(8)=\log(7)$$

Rhannu’r ddwy ochr â \log(8).

$$x+1=\frac{\log(7)}{\log(8)}$$

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

$$x+1=\log_{8}\left(7\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$x=\frac{\log_{2}\left(7\right)}{3}-1$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(2)}+\frac{\log_{2}\left(7\right)}{3}-1$$

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