Write an Exponential/Logarithmic Equation

Question

Write one variable exponential or logarithmic equations that

have the following characteristics:

a. has solutions 𝑥 = 1 and 𝑥 = 2

b. does not contain the digit “3”

c. contains the number -12.

What's the parent function I need to use to start on this?

What are two different equations that could be made and are those the only

possible answers?

Answer 1

1. 2^x = f(x)
2. if x = 1, then f(x) = 2
3. if x = 2, then f(x) = 4

(2^x - 2) (2^x - 4) = 0

= 2^2x - 6 * 2^x + 8 = 0, subtract 12 on both sides of the equation

= 2^2x - 6 * 2^x - 4 = -12

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f (x) = Log₂ (x)

1. if x = 1, f(x) = 0
2. if x = 2, f (x) = 1

Log₂ (x) (Log₂ (x) - 1) = 0

= (Log₂ (x))² - Log₂ (x) = 0, subtract both sides of the equation by 12

= (Log₂ (x))² - Log₂ (x) -12 = -12

You do not need to use 12, you can use many different values except for those with 3's.