Exponentials and Logarithms

Question 1

Draw the graph for y= -e^x

Answer 1

Question 2

Draw the graph for y=e^x

Answer 2

Question 3

Draw the graph for y = e^-x/ y = 1/a^x

^{Why are fractional exponentials like this}

Answer 3

when you multiply fractions by anything the value is always smaller

for example 0.5 X 0.5 =0.25

Question 4

Draw the graph for y = b(e^x)

for example y= 10 (e^x)

Answer 4

Question 5

Draw the graph for y = b+e^x

For example y= 3 +e^x

Answer 5

Question 6

What is the rule for differentiating exponential ?

Answer 6

if y = e^kx

dy/dx= ke^kx

Question 7

Log rules

log_ax+log_ay=?

Answer 7

log_axy

Question 8

Log rules

log_ax - log_ay=?

Answer 8

log_ax/y

Question 9

Log rules

log_axⁿ=?

Answer 9

nlog_ax

Question 10

Log rules

log_a1/x =?

Answer 10

log_ax^-1 = -1log_ax

Question 11

Log rules

log_aA=?

log_aA^b=?

Answer 11

1

b

Question 12

Log rules

log_a1

Answer 12

0

Question 13

Why does log_aA^b=?

Answer 13

because log_aA^b= blog_aA = b multiply 1 which = b

Question 14

Solve:

e^x=6

Answer 14

lne^x=ln6

x=ln6

Question 15

Solve ln(4x)=1

Answer 15

4x=e¹

x=e/4

Question 16

Solve :

3^x=11

Answer 16

Take ln (logs to base e)

ln3^x = ln11

xln3 = ln11

x= ln 11/ ln 3

Question 17

Solve

5^(x+1) = 8^(x-3)

Answer 17

Question 18

Solve:

2^2x- 6(2^x) + 5

Answer 18

Question 19

Do b

Answer 19

Question 20

Answer 20

Question 21

How do you proof that an exponential cannot exceed a certain value .

for example use equation c to work out d

Answer 21

Question 22

Why can’t you take to the log equations such as :

e^3 +e^4 = 5

Answer 22

2+3=5
but
2^2+3^2 is not equal to 5^2

The point I’m making is that some functions may not be applied ‘term by term’ to the equation. This is the same for natural logarithms.

2+3=5 but……..
ln(2)+ln(3) does not equal ln(5).

Question 23

Find the rate at which the temperature of the ball is decreasing at the instant when t=50. Give your answer in celsius per minute

Answer 23

Question 24

Answer 24

Question 25

Answer 25