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

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

Solvi għal x

$$x=13$$

Passi għall-Użu ta' Definizzjoni ta' Logaritmu

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2.

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

Ikkalkula 2 bil-power ta' 31 u tikseb 2147483648.

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

Ikkalkula 4 bil-power ta' 50 u tikseb 1267650600228229401496703205376.

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

Immultiplika 2147483648 u 1267650600228229401496703205376 biex tikseb 2722258935367507707706996859454145691648.

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

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

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

Iddividi ż-żewġ naħat b'2.

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

Iddividi 2722258935367507707706996859454145691648 b'2 biex tikseb1361129467683753853853498429727072845824.

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

Ħu l-logaritmu taż-żewġ naħat tal-ekwazzjoni.

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

Il-logaritmu ta ' numru imqajjem għall-enerġija hi l-qawwa ħinijiet Il-logaritmu tal-għadd.

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

Iddividi ż-żewġ naħat b'\log(4).

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

Bil-formula bidla tal-bażi \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

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

Iddividi ż-żewġ naħat b'5.

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

Solvi għal x (complex solution)

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

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