Datrys (7^2)^n=49.7^8

$$( 7 ^ { 2 } ) ^ { n } = 49.7 ^ { 8 }$$

Datrys ar gyfer n

$$n=4\log_{7}\left(49.7\right)\approx 8.029157842$$

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfrifo 7 i bŵer 2 a chael 49.

$$49^{n}=49.7^{8}$$

Cyfrifo 49.7 i bŵer 8 a chael 37226406026790.94258561.

$$49^{n}=37226406026790.94258561$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(49^{n})=\log(37226406026790.94258561)$$

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

$$n\log(49)=\log(37226406026790.94258561)$$

Rhannu’r ddwy ochr â \log(49).

$$n=\frac{\log(37226406026790.94258561)}{\log(49)}$$

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

$$n=\log_{49}\left(37226406026790.94258561\right)$$

Datrys ar gyfer n (complex solution)

$$n=\frac{i\pi n_{1}}{\ln(7)}-\log_{7}\left(\frac{10000}{61013446081}\right)$$

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