Solving Exponential Equations

The video tutorial guides viewers through solving an Olympiad-level math problem involving exponential equations. The instructor begins by rearranging the equation to have a common base, applies logarithms to isolate the variable x, and verifies the solution by substituting back into the original equation. The solution is confirmed to be approximately 0.46.

What is the initial equation given in the problem?

• 2^x - 3^2x = 1

• 2^x + 3^2x = 1

• 2^x - 1 + 3^2x = 0

• 2^x + 1 - 3^2x = 0

What is the first step taken to rearrange the equation?

• Add 3^2x to both sides

• Divide both sides by 3

• Subtract 2^x from both sides

• Multiply both sides by 2

According to the law of indices, how can 2^(x+1) be expressed?

• 2^x + 2^1

• 2^x * 2^1

• 2^(x+1)

• 2^(x-1) * 2^2

What operation is performed to simplify the equation further?

• Multiply both sides by 2^x

• Divide both sides by 2^x

• Add 2^x to both sides

• Subtract 2^x from both sides

What is the result of dividing 9 by 2 in the simplification process?

• 6.5

• 5.5

• 4.5

• 3.5

What mathematical operation is used to solve for x after simplification?

• Adding a constant

• Multiplying by a constant

• Taking square roots

• Taking logarithms

What is the approximate value of x found using logarithms?

• 0.46

• 0.66

• 0.56

• 0.36

What is the purpose of substituting the value of x back into the original equation?

• To simplify the equation further

• To find a new solution

• To verify the solution

• To eliminate x from the equation

What is the value of 2^1.46 approximately?

• 2.75

• 1.75

• 4.75

• 3.75

What conclusion is drawn after verifying the solution?

• The solution needs adjustment

• The solution is approximate

• The solution is incorrect

• The solution is correct