# Algebra Exponential and Sums & Difference of Logarithmic Questions

1. Determine whether the given functions are one-to-one. It they are one-to-one, find a formula for the inverse.(a)

(

x

)

=

x

+

5

(b)

(

x

)

=

x

2

4

(c)

(

x

)

=

2

x

3

5

(d)

(

x

)

=

x

5

(e)

(

x

)

=

6

x

+

5

2. Answer the following exponential and logarithmic questions(a) Use properties of logarithms to expand the logarithmic expression,

(

10

,

000

x

2

)

Then simplify.(b) Solve the equation

${}^{}$

3

x

=

81

(c) Solve the equation

${}_{}$

log

6

(

x

+

2

)

=

2

(d) Express in terms of sums and difference of logarithms

${}_{}$

log

b

(

6

x

5

y

z

2

)

(e) Expand and simplify

Maybe one or two problems on graphing