Solving Exponential equations

The video tutorial explains how to solve the equation T / 3 = .5 using logarithms. It begins by introducing the problem and discussing different methods to approach it. The tutorial then demonstrates how to apply logarithms, specifically using base 5, to simplify the equation. It further explains how to solve for T by isolating the variable and using the change of base formula. The final section covers the calculation steps to arrive at the approximate value of T, which is 1.29.

What is the first step in solving an equation with a rational exponent?

• Add the exponent to both sides

• Take the logarithm of both sides

• Multiply both sides by the exponent

• Divide both sides by the exponent

Why is the logarithm used in solving the equation?

• To multiply the exponents

• To divide the exponents

• To eliminate the base

• To add the exponents

What property of logarithms is used to simplify the equation?

• Logarithm of a power

• Logarithm of a quotient

• Logarithm of a product

• Logarithm of a sum

What is the purpose of the change of base formula in this context?

• To multiply two logarithms

• To subtract two logarithms

• To add two logarithms

• To convert the logarithm to a different base

What is the approximate value of T after applying the change of base formula?

• 2.50

• 3.14

• 0.75

• 1.29