A logarithmic function is defined by with

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

A logarithmic function

f

is defined by

f(x)=\log_a x

with

a>0,\,a\neq1

. A new function

g

is obtained by translating the graph of

f

two units to the right and three units upward. The graph of

g

passes through the point

(6,1)

. (i) Obtain the value of the base

a

. (ii) Write the explicit equation of

g(x)

. (iii) Determine the

x

-coordinate of the point where the graph of

g

cuts the

x

-axis. (iv) State whether the graph of

g

is increasing or decreasing and justify your answer from the value of

a

. Also mention its concavity.