Lahenda 4x(1+48%)^t=19

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

Lahendage ja leidke x

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

Juhised lineaarvõrrandi lahendamiseks

Taandage murd \frac{48}{100} vähimale ühiskordsele, eraldades ja taandades arvu 4.

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

Liitke 1 ja \frac{12}{25}, et leida \frac{37}{25}.

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

Võrrand on standardkujul.

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

Jagage mõlemad pooled 4\times \left(\frac{37}{25}\right)^{t}-ga.

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

4\times \left(\frac{37}{25}\right)^{t}-ga jagamine võtab 4\times \left(\frac{37}{25}\right)^{t}-ga korrutamise tagasi.

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

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

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

Lahendage ja leidke t (complex solution)

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

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

$$x\neq 0$$

Lahendage ja leidke t

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

$$x>0$$