Solve a(1+8%)^x=2

$$a ( 1 + 8 \% ) ^ { x } = 2$$

Solve for a

$$a=2\times \left(\frac{25}{27}\right)^{x}$$

Steps for Solving Linear Equation

Reduce the fraction \frac{8}{100} to lowest terms by extracting and canceling out 4.

$$a\left(1+\frac{2}{25}\right)^{x}=2$$

Add 1 and \frac{2}{25} to get \frac{27}{25}.

$$a\times \left(\frac{27}{25}\right)^{x}=2$$

The equation is in standard form.

$$\left(\frac{27}{25}\right)^{x}a=2$$

Divide both sides by \left(\frac{27}{25}\right)^{x}.

$$\frac{\left(\frac{27}{25}\right)^{x}a}{\left(\frac{27}{25}\right)^{x}}=\frac{2}{\left(\frac{27}{25}\right)^{x}}$$

Dividing by \left(\frac{27}{25}\right)^{x} undoes the multiplication by \left(\frac{27}{25}\right)^{x}.

$$a=\frac{2}{\left(\frac{27}{25}\right)^{x}}$$

Divide 2 by \left(\frac{27}{25}\right)^{x}.

$$a=2\times \left(\frac{25}{27}\right)^{x}$$

Solve for x (complex solution)

$$x=\frac{-\ln(a)+\ln(2)}{\ln(\frac{27}{25})}+\frac{2\pi n_{1}i}{\ln(\frac{27}{25})}$$

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

$$a\neq 0$$

Solve for x

$$x=\frac{-\ln(a)+\ln(2)}{\ln(\frac{27}{25})}$$

$$a>0$$