Datrys 9^n*3^5*27^3/2*21^4=27

$$\frac { 9 ^ { n } \times 3 ^ { 5 } \times 27 ^ { 3 } } { 2 \times 21 ^ { 4 } } = 27$$

Datrys ar gyfer n

$$n=\frac{\log_{3}\left(4802\right)-7}{2}\approx 0.357952375$$

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfrifo 3 i bŵer 5 a chael 243.

$$\frac{9^{n}\times 243\times 27^{3}}{2\times 21^{4}}=27$$

Cyfrifo 27 i bŵer 3 a chael 19683.

$$\frac{9^{n}\times 243\times 19683}{2\times 21^{4}}=27$$

Lluosi 243 a 19683 i gael 4782969.

$$\frac{9^{n}\times 4782969}{2\times 21^{4}}=27$$

Cyfrifo 21 i bŵer 4 a chael 194481.

$$\frac{9^{n}\times 4782969}{2\times 194481}=27$$

Lluosi 2 a 194481 i gael 388962.

$$\frac{9^{n}\times 4782969}{388962}=27$$

Rhannu 9^{n}\times 4782969 â 388962 i gael 9^{n}\times \frac{59049}{4802}.

$$9^{n}\times \frac{59049}{4802}=27$$

Lluoswch y ddwy ochr â \frac{4802}{59049}, cilyddol \frac{59049}{4802}.

$$9^{n}=27\times \frac{4802}{59049}$$

Lluosi 27 a \frac{4802}{59049} i gael \frac{4802}{2187}.

$$9^{n}=\frac{4802}{2187}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(9^{n})=\log(\frac{4802}{2187})$$

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

$$n\log(9)=\log(\frac{4802}{2187})$$

Rhannu’r ddwy ochr â \log(9).

$$n=\frac{\log(\frac{4802}{2187})}{\log(9)}$$

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

$$n=\log_{9}\left(\frac{4802}{2187}\right)$$

Datrys ar gyfer n (complex solution)

$$n=\frac{\pi n_{1}i}{\ln(3)}+\frac{\log_{3}\left(4802\right)}{2}-\frac{7}{2}$$

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