Free Printable T&T6: Ex7.9 Log Functions

1.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

2.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

3.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

4.

log (2 * 3) = ?

a)

log 2 + log 3

b)

log 2 * log 3

c)

log 2 - log 3

d)

log 5

5.

log (2 / 3) = ?

a)

log 2 + log 3

b)

log 2 / log 3

c)

log 2 - log 3

d)

2/3 * log 1

6.

log (3²) =?

a)

log 6

b)

2 log 3

c)

log₂ 3

d)

log₃ 2

7.

log (a² * b) = ?

a)

2log(a) + log(b)

b)

2log(a) + 2log(b)

c)

log(a) + log(b)

d)

2log(a) * log(b)

8.

Rewrite in exponential form:
2=log₉x

a)

9^x=2

b)

2^x=9

c)

2⁹=x

d)

9²=x

9.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

10.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

11.

Write 2³= 8 in logarithmic form.

a)

log₂ 8 = 3

b)

log₂ 3 = 8

c)

log₃ 8 = 2

d)

log₃ 2 = 8

12.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

13.

Simplify log₄4^3x

a)

3x

b)

3

c)

4

d)

4^3x

14.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

15.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

16.

log (-1) =

a)

0.1

b)

.01

c)

all real numbers

d)

does not exist

17.

Which expression is equivalent to $\log_{ }4n^3$ ?

a)

$3\left(\log4\ +\log n\right)$

b)

$3\cdot\log4\ +\log n$

c)

$\log4+3\cdot\log n$

d)

$\log64+3\cdot\log n$

18.

Which expression is equivalent to $\frac{5}{2}\cdot\log_4x\ -3\cdot\log_4y$

a)

$\log_45x^2-3y$

b)

$\log_4\ \frac{5x^2}{y^3}$

c)

$\log_45x^2y^3$

d)

$\log_4\ \frac{x^2\sqrt{x}}{y^3}$

19.

Which does not help to explain why you cannot use the laws of logarithms to expand or simplify $\log_4\left(3y-4\right)$ ?

a)

The expression $3y-4$ cannot be factored.

b)

The expression $3y-4$ is not raised to a power.

c)

$3y$ and $4$ are neither multiplied together, nor are they divided into each other.

d)

Each term in the expression does not have the same variable.

20.

Write as a single logarithm: $\log_6\left(x-3\right)+\log_6x$

a)

$\log_6\left(x^2-3x\right)$

b)

$\log_6\left(2x-3\right)$

c)

$\log_{12}\left(x^2-3x\right)$

d)

$\log_6\left(-x\right)$

21.

Which logarithm is equal to $\log_8\left(3x-1\right)-5\log_8\left(x\right)$ ?

a)

$\log_8\left(\frac{3x-1}{x^5}\right)$

b)

$\log_{16}\left(\frac{3x-1}{x^5}\right)$

c)

$\log_8\left(\frac{3x-1}{5x}\right)$

d)

$\log_8\left(x^5+3x-1\right)$

T&T6: Ex7.9 Log Functions

Total questions: 21

Worksheet time: 18mins

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