Problem 7
Determine the value of $x$ from $\sqrt[4]{3^{x^2}\sqrt{3^{x - 1}}} = \sqrt[8]{9^{x + 1}}$
 

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

3. 9^x - 6(9^-x) - 1 = 0
4. 2^{x + 1} · 3^x = 5^{x + 3}

Solve for x from the following:

1. $\log_6 (x - 2) + \log_6 (x + 3) = 1$
    
2. $x^{\log x} = 10\,000$

Problem
Solve for $x$ and $y$ from the given system of equations.
$\dfrac{3}{x^2} - \dfrac{4}{y^2} = 2$   ←   Equation (1)

$\dfrac{5}{x^2} - \dfrac{3}{y^2} = \dfrac{17}{4}$   ←   Equation (2)
 

Problem
Solve for $x$ and $y$ from the given system of equations.
$x^2y + y = 17$   ←   Equation (1)

$x^4y^2 + y^2 = 257$   ←   Equation (2)
 

Problem
Solve for x and y from the given system of equations.
$x + 2y = 6$   ←   Equation (1)

$\sqrt{x} + \sqrt{y} = 3$   ←   Equation (2)
 

Solve for $x$ from the following equations:

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

Determine the value of $x$ from the following equations:

3. $\sqrt{(4 - x^2)^3} + 3x^2\sqrt{4 - x^2} = 0$
    
4. $\dfrac{1}{3x - 2} - \dfrac{8}{\sqrt{3x - 2}} = 9$
    

Solve for $x$ from the following equations

1. $\sqrt{3 - x} + \sqrt{4 - 2x} = \sqrt{3 - 3x}$
    
2. $\sqrt{\dfrac{2x + 4}{x - 5}} + 8\sqrt{\dfrac{x - 5}{2x + 4}} = 6$

Problem 3
A man bought a cellphone and laptop for P50,000.00, paying three times as much for the laptop as for the cellphone. How much did each cost?
 

Problem 4
Two boys, counting their money, found that together they had P372, and that Rody had five times as much as Mar. How much had each?