exponential equation

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:

  1. 9x - 6(9-x) - 1 = 0
  2. 2x + 1 · 3x = 5x + 3

 

03 - Solved Problems Involving Exponents and Radicals

Solve for $x$ from the following equations:

  1. $\left( \dfrac{x^2 - 15}{x} \right)^2 - 16\left( \dfrac{15 - x^2}{x} \right) + 28 = 0$
     
  2. $\dfrac{x}{\sqrt{x} + \sqrt{9 - x}} + \dfrac{x}{\sqrt{x} - \sqrt{9 - x}} = \dfrac{24}{\sqrt{x}}$

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)
 

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