Solving Exponential Equations with Logarithms

The video tutorial covers solving exponential equations by converting bases and using logarithms. It demonstrates solving equations without logs by changing bases and equating exponents. The tutorial also explains using logarithms to solve equations when base conversion is not feasible. Additionally, it covers solving quadratic equations derived from exponential forms and using factoring and substitution techniques for complex equations.

How can you solve an exponential equation with different bases without using logarithms?

• By adding the exponents directly

• By converting both sides to a common base

• By subtracting the bases

• By dividing one side by the other

What is the common base used to solve the equation 8 raised to the 4x minus 12 equals 16 raised to the 5x minus 3?

• Base 16

• Base 2

• Base 4

• Base 8

What is the result of 3 raised to the power of x equals 8 when solved using logarithms?

• x = 1.8928

• x = 2.0794

• x = 3.1415

• x = 4.0829

When solving an equation with base e, which logarithm is preferable to use?

• Common logarithm

• Binary logarithm

• Base 10 logarithm

• Natural logarithm

What is the exact value of x when e raised to the x equals 7?

• ln 7

• 7^e

• e^7

• log 7

What is the value of x when 5 plus 4 raised to the power of x minus 2 equals 23?

• x = 5.0629

• x = 4.08496

• x = 3.14159

• x = 2.08496

How do you solve an equation where an exponential term is equal to a fraction?

• By converting the fraction to a decimal

• By finding a common base for the fraction and the exponential term

• By using logarithms to eliminate the exponent

• By multiplying both sides by the denominator of the fraction

How do you solve an equation with an exponential term on one side and a constant on the other without using logarithms?

• By subtracting the exponential term from both sides

• By adding the constant to both sides

• By dividing both sides by the base of the exponential term

• By converting the constant to an exponential form with the same base

What technique is used to solve an equation that can be reduced to a quadratic form?

• Using the quadratic formula

• Factoring by substitution

• Factoring by grouping

• Completing the square

What is the value of x when 3 to the 2x minus 3 to the 2x minus 1 equals 18?

• x = 2

• x = 2.5

• x = 3

• x = 1.5