# Exponential Equation

**Problem**

A germ population has a growth curve $Ae^{0.4t}$. At what value of $t$ does its original value doubled?

A. t = 7.13 |
C. t = 1.73 |

B. t = 1.37 |
D. t = 3.71 |

## 04 - Solution of Radical Equation

**Problem 7**

Determine the value of $x$ from $\sqrt[4]{3^{x^2}\sqrt{3^{x - 1}}} = \sqrt[8]{9^{x + 1}}$

## 02 - Solution to Equations Involving Variable Exponent

Solve for the value of x from each of the following equations:

- 9
^{x}- 6(9^{-x}) - 1 = 0 - 2
^{x + 1}· 3^{x}= 5^{x + 3}

## 03 - Solved Problems Involving Exponents and Radicals

Solve for $x$ from the following equations:

- $\left( \dfrac{x^2 - 15}{x} \right)^2 - 16\left( \dfrac{15 - x^2}{x} \right) + 28 = 0$

- $\dfrac{x}{\sqrt{x} + \sqrt{9 - x}} + \dfrac{x}{\sqrt{x} - \sqrt{9 - x}} = \dfrac{24}{\sqrt{x}}$

## Example 01 - Simultaneous Non-Linear Equations of Three Unknowns

**Problem**

Solve for *x*, *y*, and *z* from the following simultaneous equations.

$z^x \, z^y = 100\,000$ ← equation (1)

$(z^x)^y = 100\,000$ ← equation (2)

$\dfrac{z^x}{z^y} = 10$ ← equation (3)