Exponential Equation
Example 05 - Simultaneous Non-Linear Equations of Three Unknowns
Problem
Solve for x, y, and z from the following simultaneous equations.
$x^2 - yz = 3$ ← Equation (1)
$y^2 - xz = 4$ ← Equation (2)
$z^2 - xy = 5$ ← Equation (3)
04 - Solution of Radical Equation
Problem 7
Determine the value of $x$ from $\sqrt[4]{3^{x^2}\sqrt{3^{x - 1}}} = \sqrt[8]{9^{x + 1}}$
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Solution to Equations Involving Variable Exponent
Solve for the value of x from each of the following equations:
- 9x - 6(9-x) - 1 = 0
- 2x + 1 · 3x = 5x + 3
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03 - Solved Problems Involving Exponents and Radicals
Solve for $x$ from the following equations:
- $\left( \dfrac{x^2 - 15}{x} \right)^2 - 16\left( \dfrac{15 - x^2}{x} \right) + 28 = 0$
- $\dfrac{x}{\sqrt{x} + \sqrt{9 - x}} + \dfrac{x}{\sqrt{x} - \sqrt{9 - x}} = \dfrac{24}{\sqrt{x}}$
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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)
