Datrys 2^31*4^50div2=4^5x

$${ 2 }^{ 31 } \times { 4 }^{ 50 } \div 2= { 4 }^{ 5x }$$

Datrys ar gyfer x

$$x=13$$

Camau gan Ddefnyddio Diffiniad Logarithm

Lluoswch ddwy ochr yr hafaliad â 2.

$$2^{31}\times 4^{50}=2\times 4^{5x}$$

Cyfrifo 2 i bŵer 31 a chael 2147483648.

$$2147483648\times 4^{50}=2\times 4^{5x}$$

Cyfrifo 4 i bŵer 50 a chael 1267650600228229401496703205376.

$$2147483648\times 1267650600228229401496703205376=2\times 4^{5x}$$

Lluosi 2147483648 a 1267650600228229401496703205376 i gael 2722258935367507707706996859454145691648.

$$2722258935367507707706996859454145691648=2\times 4^{5x}$$

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

$$2\times 4^{5x}=2722258935367507707706996859454145691648$$

Rhannu’r ddwy ochr â 2.

$$4^{5x}=\frac{2722258935367507707706996859454145691648}{2}$$

Rhannu 2722258935367507707706996859454145691648 â 2 i gael 1361129467683753853853498429727072845824.

$$4^{5x}=1361129467683753853853498429727072845824$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(4^{5x})=\log(1361129467683753853853498429727072845824)$$

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

$$5x\log(4)=\log(1361129467683753853853498429727072845824)$$

Rhannu’r ddwy ochr â \log(4).

$$5x=\frac{\log(1361129467683753853853498429727072845824)}{\log(4)}$$

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

$$5x=\log_{4}\left(1361129467683753853853498429727072845824\right)$$

Rhannu’r ddwy ochr â 5.

$$x=\frac{65}{5}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\pi n_{1}}{5\ln(2)}+13$$

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