Datrys 2*16^2n=70

$$2 \cdot 16 ^ { 2 n } = 70$$

Datrys ar gyfer n

$$n=\frac{\log_{2}\left(35\right)}{8}\approx 0.641160377$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$2\times 16^{2n}=70$$

Rhannu’r ddwy ochr â 2.

$$16^{2n}=35$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(16^{2n})=\log(35)$$

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

$$2n\log(16)=\log(35)$$

Rhannu’r ddwy ochr â \log(16).

$$2n=\frac{\log(35)}{\log(16)}$$

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

$$2n=\log_{16}\left(35\right)$$

Rhannu’r ddwy ochr â 2.

$$n=\frac{\log_{2}\left(35\right)}{2\times 4}$$

Datrys ar gyfer n (complex solution)

$$n=\frac{\pi n_{1}i}{4\ln(2)}+\frac{\log_{2}\left(35\right)}{8}$$

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