Datrys (33^7)^4/3^3=3^5*x

$$\frac { ( 33 ^ { 7 } ) ^ { 4 } } { 3 ^ { 3 } } = 3 ^ { 5 \cdot x }$$

Datrys ar gyfer x

$$x=\frac{28\log_{3}\left(11\right)}{5}+5\approx 17.222886696$$

Camau gan Ddefnyddio Diffiniad Logarithm

I godi pŵer rhif i bŵer arall, lluoswch yr esbonyddion. Lluoswch 7 a 4 i gael 28.

$$\frac{33^{28}}{3^{3}}=3^{5x}$$

Cyfrifo 33 i bŵer 28 a chael 3299060778251569566188233498374847942355841.

$$\frac{3299060778251569566188233498374847942355841}{3^{3}}=3^{5x}$$

Cyfrifo 3 i bŵer 3 a chael 27.

$$\frac{3299060778251569566188233498374847942355841}{27}=3^{5x}$$

Rhannu 3299060778251569566188233498374847942355841 â 27 i gael 122187436231539613562527166606475849716883.

$$122187436231539613562527166606475849716883=3^{5x}$$

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

$$3^{5x}=122187436231539613562527166606475849716883$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{5x})=\log(122187436231539613562527166606475849716883)$$

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

$$5x\log(3)=\log(122187436231539613562527166606475849716883)$$

Rhannu’r ddwy ochr â \log(3).

$$5x=\frac{\log(122187436231539613562527166606475849716883)}{\log(3)}$$

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

$$5x=\log_{3}\left(122187436231539613562527166606475849716883\right)$$

Rhannu’r ddwy ochr â 5.

$$x=\frac{\log_{3}\left(122187436231539613562527166606475849716883\right)}{5}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{5\ln(3)}+\frac{28\log_{3}\left(11\right)}{5}+5$$

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