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### Course: Precalculus (Eureka Math/EngageNY)>Unit 3

Lesson 15: Topic C: Lessons 20-21: Inverse relationship of exponentials and logarithms

# Relationship between exponentials & logarithms: tables

Given incomplete tables of values of b^x and its corresponding inverse function, log_b(y), Sal uses the inverse relationship of the functions to fill in the missing values. Created by Sal Khan.

## Want to join the conversation?

• Is it necessary to include parenthesis around the base number?
• It is required sometimes, but you can write it whatever way you want on your own.
• In the table, b is proved to be 2. We all know that 2 raised to power 3 is 8. In the table, 2 raised to power 2.822 is 7, close to 8. But the next power, 2.169, is less than 2.822 but still produced the number 9. How is it possible? Is there some kind of mistake or what? Was it 3, accidentally written as 2?
• I think so.
• How would you calculate a decimal exponent?
• You will first have to break up the exponents so that you will reduce the number of numbers with decimals as exponents. Solve the numbers with integral exponents. Then, turn the decimals exponents to fraction exponents. Let's say the number is 4^(1/2). Then you would take the square root (since it is 1/2) of the base. If it was 4^(1/3), then you would take the cube root and so on. Please let me know if I have answered your question.
• How would you graph these?
• There is a video called "Plotting points of logarithmic function". I'd check it out first and see if that clears anything up.(:
• - why are both sides divided by 10 rather than 5?
• We have 10d = 5. We essentially want to islote d. If we divide by 5, we get 2d = 1. See that d still isn't isolated. Hence, we divide by 10 to get d = 1/2.
• Not sure how in the first table 2 raise to 2.169 equals to 9 (Last column) .. It should be 4.5 isn't it? Or am I missing something
• You missed the pop-up box in the lower right-hand corner that appears at which indicates that the entry should be 3.169, not 2.169.
(Note that 2 TIMES 4.5 is 9, but in this problem we are raising 2 to the POWER of 3.169.)
• I think the number in the first graph's fifth column is wrong.
2^2.169 is 4.497, 2^3.169 is 8.994, so it should be 3.169 instead of 2.169.
• Even if it was to be meant 2.169, then the value of b^x must be equal to 4.5
(1 vote)
• When solving for c, I got to 2^1.585=2c, and then divided both sides by 2, so I had: (2^1.585)/(2^1) = c. Then I just got 2^0.585 = c by subtracting the exponents. I know that we don't know what 2^0.585 equals without a calculator, but is that a valid approach?