Datrys 2^n-1=1/32

$$2 ^ { n - 1 } = \frac { 1 } { 32 }$$

Datrys ar gyfer n

$$n=-4$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$2^{n-1}=\frac{1}{32}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{n-1})=\log(\frac{1}{32})$$

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

$$\left(n-1\right)\log(2)=\log(\frac{1}{32})$$

Rhannu’r ddwy ochr â \log(2).

$$n-1=\frac{\log(\frac{1}{32})}{\log(2)}$$

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

$$n-1=\log_{2}\left(\frac{1}{32}\right)$$

Adio 1 at ddwy ochr yr hafaliad.

$$n=-5-\left(-1\right)$$

Datrys ar gyfer n (complex solution)

$$n=\frac{i\times 2\pi n_{1}}{\ln(2)}-4$$

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