Chapter 13 Exponentials and Logarithms

Question 1

What is the y-axis intercept in the equation logy = (loga)x + logk?

Answer 1

log k

This represents the value of log y when x is zero.

Question 2

What is the gradient when plotting log y against x?

Answer 2

log a

This indicates the slope of the line in the plot.

Question 3

What is the equation for plotting log y against log x?

Answer 3

logy = nlogx + logk

Here, n is the gradient of the line.

Question 4

What is the logarithm of a number to its own base?

Answer 4

log_a a = 1

This means that the logarithm of a number to its own base equals one.

Question 5

What is the logarithm of 1?

Answer 5

log 1 = 0

This indicates that the logarithm of one is always zero.

Question 6

What is the rule for the division of logarithms?

Answer 6

log(x/y) = log x - log y

This shows how to express the logarithm of a quotient.

Question 7

What is the rule for the multiplication of logarithms?

Answer 7

log(xy) = log x + log y

This indicates how to express the logarithm of a product.

Question 8

What is the natural logarithm of x denoted as?

Answer 8

ln x

This is the logarithm to the base e.

Question 9

What is the relationship between exponential functions and logarithms?

Answer 9

A function of the form y = a^x is described as exponential.

This indicates that exponential functions are inversely related to logarithmic functions.

Question 10

What is the differential of e^kx ?

Answer 10

dy/dx = k e^kx

Question 11

What is the power law for logs?

Answer 11

log x^n = n log x