Logarithmic and Exponential Functions

The video tutorial explains how to solve an exponential equation by applying exponent properties and converting it into a logarithmic form. It demonstrates the use of the power to power and product to power properties to simplify the equation. The tutorial then shows how to find the exact solution using logarithms and the approximate solution using the change of base formula. The process is detailed step-by-step, ensuring clarity in understanding the mathematical concepts involved.

What is the initial exponential equation given in the problem?

• 3^x * 4^x = 48

• 3^x * 4^2x = 48

• 3^x * 4^2x = 15

• 3^x * 4^x = 15

Why can't the two exponential terms be multiplied directly?

• The bases are the same but the exponents are different.

• The bases and exponents are both different.

• The bases are different and the exponents are the same.

• The bases and exponents are both the same.

What is the result of applying the power to power property to 4^(2x)?

• 4^2

• 4^2x

• 16^x

• 4^x

What is the simplified form of 3^x * 16^x using the product to power property?

• 48^x

• 3^x * 16^x

• 3 * 16

• 48

What is the equivalent logarithmic equation for 48^x = 15?

• log base 15 of 48 = x

• log base x of 48 = 15

• log base 48 of 15 = x

• log base x of 15 = 48

What is the exact solution for x in the equation 48^x = 15?

• x = log base 15 of 15

• x = log base 48 of 15

• x = log base 48 of 48

• x = log base 15 of 48

What is the base used in the logarithmic equation derived from 48^x = 15?

• 15

• 16

• 48

• x

Which formula is used to find the approximate solution to four decimal places?

• Logarithmic conversion formula

• Product to power formula

• Power to power formula

• Change of base formula

What is the approximate value of x using the natural log in the change of base formula?

• 0.69999

• 0.6999

• 0.7001

• 0.7000

What is the result of using the common log in the change of base formula for x?

• Approximately 0.69999

• Approximately 0.6999

• Approximately 0.7001

• Approximately 0.7000