Using one to one property with different bases to solve an exponential equation

The video tutorial covers solving a logarithmic equation by rewriting it to have the same base. Initially, the problem is introduced, and a common approach using logarithms is discussed. However, the instructor explains why this approach doesn't work and demonstrates how to rewrite the equation with the same base using the power rule of exponents. The solution is then derived by equating the exponents, leading to the final answer.

What is the initial problem discussed in the video?

• log base three to the X + 2 = 27

• log base two to the X + 3 = 27

• log base three to the X + 3 = 27

• log base five to the X + 2 = 27

Why can't we simply take the log of 27 on one side of the equation?

• Because 27 is already simplified

• Because it would not be applied to both sides equally

• Because it would not affect the equation

• Because 27 is not a power of 3

How can 27 be rewritten to have the same base as 3?

• 3^2

• 3^4

• 3^5

• 3^3

What mathematical property allows us to equate the exponents once the bases are the same?

• Associative property

• Power rule of exponents

• One-to-one property

• Distributive property

What is the final value of X in the equation?

• One half

• Two thirds

• Three fourths

• Two fifths