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

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

Solve for x

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

Steps for Solving Linear Equation

Reduce the fraction \frac{48}{100} to lowest terms by extracting and canceling out 4.

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

Add 1 and \frac{12}{25} to get \frac{37}{25}.

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

The equation is in standard form.

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

Divide both sides by 4\times \left(\frac{37}{25}\right)^{t}.

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

Dividing by 4\times \left(\frac{37}{25}\right)^{t} undoes the multiplication by 4\times \left(\frac{37}{25}\right)^{t}.

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

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

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

Solve for t (complex solution)

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

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

$$x\neq 0$$

Solve for t

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

$$x>0$$