Riješi 4x(1+48%)^t=19

$$4 x ( 1 + 48 \% ) ^ { t } = 19$$

Izračunaj x

$$x=\frac{19\times \left(\frac{25}{37}\right)^{t}}{4}$$

Koraci rješavanja linearne jednadžbe

Skratite razlomak \frac{48}{100} na najmanje vrijednosti tako da izlučite i poništite 4.

$$4x\left(1+\frac{12}{25}\right)^{t}=19$$

Dodajte 1 broju \frac{12}{25} da biste dobili \frac{37}{25}.

$$4x\times \left(\frac{37}{25}\right)^{t}=19$$

Jednadžba je u standardnom obliku.

$$4\times \left(\frac{37}{25}\right)^{t}x=19$$

Podijelite obje strane sa 4\times \left(\frac{37}{25}\right)^{t}.

$$\frac{4\times \left(\frac{37}{25}\right)^{t}x}{4\times \left(\frac{37}{25}\right)^{t}}=\frac{19}{4\times \left(\frac{37}{25}\right)^{t}}$$

Dijeljenjem s 4\times \left(\frac{37}{25}\right)^{t} poništava se množenje s 4\times \left(\frac{37}{25}\right)^{t}.

$$x=\frac{19}{4\times \left(\frac{37}{25}\right)^{t}}$$

Podijelite 19 s 4\times \left(\frac{37}{25}\right)^{t}.

$$x=\frac{19\times \left(\frac{25}{37}\right)^{t}}{4}$$

Izračunaj t (complex solution)

$$t=\frac{-\ln(x)+\ln(\frac{19}{4})}{\ln(\frac{37}{25})}+\frac{2\pi n_{1}i}{\ln(\frac{37}{25})}$$

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

$$x\neq 0$$

Izračunaj t

$$t=\frac{-\ln(x)+\ln(\frac{19}{4})}{\ln(\frac{37}{25})}$$

$$x>0$$