1.49: Logarithmic equations and exponential equations

4PM1/2/June/2018 — Question 4 · 9 marks

(a) Find the exact value of the root of the equation

e^{3x}=8

Give your answer in the form

\ln a

, where

a

is an integer. (2)

The curve

C_1

has equation

y=2e^{3x}

and the curve

C_2

has equation

y=(e^{3x}-4)^2

The curves

C_1

and

C_2

intersect at the points

P

and

Q

(b) Use algebra to find the exact coordinates of the points

P

and

Q

. (5)

PQ

. (2)