Solving Exponential Equations with Logarithms

The video tutorial explains how to solve an exponential equation by isolating the exponential part, applying logarithms, and using logarithmic properties to solve for X. The exact solution is expressed using logarithms, and a decimal approximation is calculated using a calculator. The process involves rearranging the equation, applying the power property of logarithms, and simplifying the equation to find the value of X, which is approximately -5.2135.

What is the primary mathematical tool needed to solve the exponential equation exactly?

• Logarithms

• Calculus

• Trigonometry

• Algebraic manipulation

What is the first step in rearranging the exponential equation?

• Multiply both sides by 5

• Subtract 1.12 from both sides

• Add 7/5 to both sides

• Divide both sides by 5

After dividing both sides by 1.12 to the power of x, what does the right side simplify to?

• 1.05

• 1

• 7/5

• 0

What property of logarithms allows us to move the exponent to the front?

• Change of base property

• Power property

• Product property

• Quotient property

Which logarithm is used in the video to solve the equation?

• Binary log

• Natural log

• Common log

• Base 10 log

What mathematical operation is performed to both sides of the equation to isolate x?

• Division

• Addition

• Subtraction

• Multiplication

How can the exact value of x be expressed using logarithms?

• As a quotient of two logs

• As a difference of two logs

• As a product of two logs

• As a sum of two logs

What is the result of dividing the logarithm of 7/5 by the logarithm of 1.05/1.12?

• The base of the logarithm

• The approximate value of x

• The exact value of x

• The power of x

What is the purpose of using the calculator in the final step?

• To simplify the equation

• To check for errors

• To verify the exact solution

• To find a decimal approximation

What is the approximate value of x after rounding to four decimal places?

• -5.2315

• -5.3125

• -5.1235

• -5.2135