Exponential Equation Using Logarithms

Solving exponential equations using logarithms: Find the value of x in the equation 4^x = 64 using logarithms

• 16

• 3

• 8

• 2

Converting exponential to logarithmic form: Write the logarithmic form of the exponential equation 3^x = 27

• log3(3) = x

• log3(9) = x

• log27(3) = x

• log3(27) = x

Converting exponential to logarithmic form: Convert the exponential equation 5^2 = 25 to logarithmic form

• log2(25) = 5

• log5(2) = 25

• log25(5) = 2

• log5(25) = 2

Using logarithms to solve real-world problems: A population of bacteria doubles every 3 hours. If there are 100 bacteria initially, how many will there be after 12 hours?

• 1600

• 1200

• 800

• 200

Understanding the relationship between exponential and logarithmic functions: Explain the relationship between the exponential function f(x) = 3^x and its corresponding logarithmic function

• They are inverse functions of each other.

• They have no relationship

• The exponential function is a subset of the logarithmic function

• They are parallel functions

log₆(2x + 3) = 3

• x = 106.5

• x = 100

• x = 16

• x = 50

Find the inverse of y=9^x

• y=log_x9

• y=log₁₀9

• x=log_y9

• y=log₉x

Write b^k = m into logarithmic form.

• log _b m = k

• log _m k = b

• log _b k = m

• log _k m = b

Using logarithms to solve real-world problems: The value of a car depreciates by 10% each year. If the initial value of the car is $20,000, what will be its value after 5 years?

• The value of the car after 5 years will be $25,000.

• The value of the car after 5 years will be $18,000.

• The value of the car after 5 years will be $12,861.30.

• The value of the car after 5 years will be $22,000.