Understanding Logarithmic Equations

The video tutorial demonstrates how to prove that log base 4 of x equals 12 times log base 2 of x. It begins by converting the logarithmic equation into an exponential form, simplifying it, and then rewriting it back as a logarithmic equation. The proof is completed by showing the equivalence graphically, confirming that both functions produce the same graph.

What is the initial step in proving that log base 4 of x equals 12 times log base 2 of x?

• Convert log base 4 of x into an exponential equation

• Graph the functions on a coordinate plane

• Multiply both sides by 12

• Express 4 as 2 squared

How is the number 4 expressed in the process of rewriting the exponential equation?

• As 2 squared

• As 2 cubed

• As 2 to the power of 4

• As 2 to the power of 1

What is the result of converting the exponential equation back into a logarithmic form?

• log base 2 of x equals y

• log base 2 of x equals 2y

• log base 4 of x equals 2y

• log base 4 of x equals y

What operation is performed to show the equivalence of the two logarithmic expressions?

• Divide both sides by 12

• Add 12 to both sides

• Multiply both sides by 12

• Subtract 12 from both sides

How can the equivalence of the two logarithmic expressions be visually confirmed?

• By using a calculator

• By solving the equation algebraically

• By checking with a table of values

• By graphing both functions on a coordinate plane