Solve 4x(1+4.8%)^t=19

$$4 x ( 1 + 4.8 \% ) ^ { t } = 19$$

Solve for x

$$x=\frac{19\times \frac{125}{131}^{t}}{4}$$

Steps for Solving Linear Equation

Expand \frac{4.8}{100} by multiplying both numerator and the denominator by 10.

$$4x\left(1+\frac{48}{1000}\right)^{t}=19$$

Reduce the fraction \frac{48}{1000} to lowest terms by extracting and canceling out 8.

$$4x\left(1+\frac{6}{125}\right)^{t}=19$$

Add 1 and \frac{6}{125} to get \frac{131}{125}.

$$4x\times \left(\frac{131}{125}\right)^{t}=19$$

The equation is in standard form.

$$4\times \left(\frac{131}{125}\right)^{t}x=19$$

Divide both sides by 4\times \left(\frac{131}{125}\right)^{t}.

$$\frac{4\times \left(\frac{131}{125}\right)^{t}x}{4\times \left(\frac{131}{125}\right)^{t}}=\frac{19}{4\times \left(\frac{131}{125}\right)^{t}}$$

Dividing by 4\times \left(\frac{131}{125}\right)^{t} undoes the multiplication by 4\times \left(\frac{131}{125}\right)^{t}.

$$x=\frac{19}{4\times \left(\frac{131}{125}\right)^{t}}$$

Divide 19 by 4\times \left(\frac{131}{125}\right)^{t}.

$$x=\frac{19\times \left(\frac{125}{131}\right)^{t}}{4}$$

Solve for t (complex solution)

$$t=\frac{-\ln(x)+\ln(4.75)}{\ln(1.048)}+\frac{i\times 2\pi n_{1}}{\ln(1.048)}$$

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

$$x\neq 0$$

Solve for t

$$t=\frac{-\ln(x)+\ln(4.75)}{\ln(1.048)}$$

$$x>0$$