6.1 (LOGS)

Question 1

a^x=b is the same as?

Answer 1

log a(b)=x

Question 2

log a (a^x)=x is the same as?

Answer 2

a^log a (x) = x

Question 3

Evaluate log 2(64sqrt(2))

Answer 3

LET x= log 2(64sqrt(2))
2^x = 64 sqrt(2)
2^x= 2^6 + 2^(1/2)
x= 13/2

Question 4

(log x)^2 ≠ log x^2 recite

Answer 4

(log x)^2 ≠ log x^2

Question 5

What is e?

Answer 5

The exponential function is y = e^x
e is an irrational number
e ≈ 2.718

Question 6

What makes e special?

Answer 6

y = e^x has the particular property

ie for every real number x, the gradient of y = e^x is also equal to e^x (see Derivatives of Exponential Functions)
The gradient is equal to y at all points on the graph