Free Printable 7.4 Precal log and exp exam

1.

Rewrite each expression as a single logarithm.

\log_25\ +\ \log_2x\ =

a)

$\log_25^x$

b)

$\log_2\ x^5$

c)

$\log_2\left(\frac{5}{x}\right)$

d)

$\log_2\ 5x$

2.

Rewrite each expression as a single logarithm.

2\log_23\ +\ 4\log_2y\ =

a)

$\log_2\left(9y^4\right)$

b)

$\log_2\ \left(6y^4\right)$

c)

$\log_2\left(\frac{9}{y^4}\right)$

d)

$\log_2\ \left(3y^4\right)$

3.

Rewrite each expression as a single logarithm.

3\log_3x\ +\ 4\log_3y\ \ +\ 2\log_3z=

a)

$\log_3\left(24xyz\right)$

b)

$\log_3\ \left(\frac{12xy}{z}\right)$

c)

$\log_3\left(x^3y^4z^2\right)$

d)

$\log_3\ \left(12xyz^2\right)$

4.

Rewrite each expression as a single logarithm.

3\log_3x\ -\ 4\log_32\ \ =

a)

$\log_3\left(16x^3\right)$

b)

$\log_3\ \left(\frac{x^3}{2}\right)$

c)

$\log_3\ \left(\frac{x^3}{8}\right)$

d)

$\log_3\ \left(\frac{x^3}{16}\right)$

5.

Expand each expression to as many logarithms as possible

\log_2xy^3\ =

a)

$3\log_2\left(xy\right)$

b)

$\log_2\ \left(xy\right)$

c)

$\log_2\ \left(x\right)\ +3\ \log_2y$

d)

$\log_2\ \left(3xy\right)$

6.

Expand each expression to as many logarithms as possible

\log_3\ \left(\frac{xy}{9z}\right)=

a)

$\log_3\ \left(xy\right)\ -\ 9\log_3\ \left(z\right)$

b)

$\log_3\ \left(xy\right)\ -\ 2\log_3\ \left(z\right)$

c)

$\log_3\ \left(xy\right)\ -\ \log_3\ \left(9z\right)$

d)

$\log_{3\ }x\ +\ \log_3\ y\ -2\ -\ \log_3\ z$

7.

Expand each expression to as many logarithms as possible

\ln_{ }\ \left(\frac{x^2y}{wz^5}\right)=

a)

$2\ln\ \left(x\right)\ +\ln\ \left(y\right)-\ \ln\ \left(w\right)\ -5\ \ln\ \left(z\right)$

b)

$\ln\left(x^2y\right)\ -\ \ln\ \left(wz^5\right)$

c)

$2\ln\left(xy\right)\ -\ 5\ln\ \left(wz\right)$

d)

$2\ln\left(x\right)\ -\ 5\ln\ \left(z\right)$

8.

Solve the log equation

\log_3x\ =\ 5

a)

$x\ =27$

b)

$x\ =81$

c)

$x\ =\ 243$

d)

$x\ =\ 729$

9.

Solve the log equation

5\ -\ 2\ \log_4\ x=\ 2

a)

$x\ =10$

b)

$x\ =8$

c)

$x\ =\ 6$

d)

$x\ =\ 12$

10.

Solve the log equation

\log_2\ x\ +\log_2\ \left(x-4\right)=\ 5

a)

$x\ =10$

b)

$x\ =8$

c)

$x\ =\ 6$

d)

$x\ =\ 12$

11.

Solve the exponential equation

2^x=\ 8

a)

$x\ =\ 3$

b)

$x=4$

c)

$x\ =\ 2$

d)

$x\ =\ 1$

12.

Solve the log equation

\log_x\ \left(125\right)=\ 3

a)

$x\ =2$

b)

$x\ =3$

c)

$x\ =\ 5$

d)

$x\ =\ 125$

13.

$\ Evaluate\ \ \ \ \log_{27}\ 9$

a)

$3$

b)

$\frac{2}{3}$

c)

$27$

d)

$\frac{1}{3}$

14.

$Evaluate\ \ \ \ \ \log_3\ \left(\frac{1}{81}\right)$

a)

$4$

b)

$-3$

c)

$-2$

d)

$-4$

15.

$Evaluate\ \ \ \ \ \log_{3\ }\sqrt{3}$

a)

$2$

b)

$\frac{1}{2}$

c)

$-\frac{1}{2}$

d)

$-2$

16.

$Evaluate\ \ \ \ \ \log_2256$

a)

$2$

b)

$4$

c)

$8$

d)

$6$

17.

$Evaluate\ \ \log_39$

a)

$2$

b)

$\frac{1}{2}$

c)

$\frac{1}{3}$

d)

$3$

18.

$Evaluate\ \ \log_93$

a)

$2$

b)

$\frac{1}{2}$

c)

$\frac{1}{3}$

d)

$3$

19.

$Evaluate\ \ \log_327$

a)

$2$

b)

$\frac{1}{2}$

c)

$\frac{1}{3}$

d)

$3$

20.

$Evaluate\ \ \log_3\left(\frac{1}{3}\right)$

a)

$\frac{1}{3}$

b)

$-\frac{1}{2}$

c)

$-1$

d)

$3$

21.

$Evaluate\ \ \log_3\left(1\right)$

a)

$-2$

b)

$-\frac{1}{2}$

c)

$0$

d)

$3$

22.

$Evaluate\ \ \log_3\left(1\right)$

a)

$-2$

b)

$-\frac{1}{2}$

c)

$0$

d)

$3$

23.

$Evaluate\ \ \log_2\left(4\right)$

a)

$4$

b)

$\frac{1}{2}$

c)

$2$

d)

$\frac{1}{3}$

24.

$Evaluate\ \ \log_2\left(128\right)$

a)

$8$

b)

$6$

c)

$7$

d)

$3$

25.

$Evaluate\ \ \ln\left(\sqrt{e}\right)$

a)

$e$

b)

$2$

c)

$1$

d)

$\frac{1}{2}$

26.

$Evaluate\ \ \log_2\left(\frac{1}{2}\right)$

a)

$-1$

b)

$-2$

c)

$-4$

d)

$-3$

27.

$Evaluate\ \ \ln\left(e\right)^2$

a)

$e$

b)

$2$

c)

$1$

d)

$\frac{1}{2}$

28.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

29.

Simplify without a calculator:

4^{-1}

a)

$\frac{1}{2}$

b)

$4$

c)

$2$

d)

$\frac{1}{4}$

30.

Simplify without a calculator:

4^{-2}

a)

$\frac{1}{16}$

b)

$8$

c)

$16$

d)

$\frac{1}{8}$

31.

Simplify without a calculator:

4^0

a)

$4$

b)

$0$

c)

$1$

d)

$\frac{1}{4}$

32.

Simplify without a calculator:

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

a)

$\frac{3}{5}$

b)

$0$

c)

$\frac{9}{25}$

d)

$\frac{5}{3}$

33.

Simplify without a calculator:

\left(100\right)^{\frac{1}{2}}

a)

$10$

b)

$10,000$

c)

$1$

d)

$\frac{1}{10}$

34.

Simplify without a calculator:

\left(100\right)^{\frac{3}{2}}

a)

$10$

b)

$10,000$

c)

$1000$

d)

$100,000$

35.

Simplify without a calculator:

\left(100\right)^{-\frac{1}{2}}

a)

$\frac{1}{1000}$

b)

$\frac{1}{30}$

c)

$1000$

d)

$\frac{1}{10}$

36.

Simplify without a calculator:

\left(125\right)^{\frac{1}{3}}

a)

$10$

b)

$5$

c)

$250$

d)

$25$

37.

Simplify without a calculator:

\left(125\right)^{\frac{2}{3}}

a)

$10$

b)

$5$

c)

$250$

d)

$25$

38.

Simplify without a calculator:

\left(100\right)^{-\frac{3}{2}}

a)

$\frac{1}{1000}$

b)

$\frac{1}{30}$

c)

$1000$

d)

$\frac{1}{10}$

39.

Simplify without a calculator:

\left(125\right)^{-\frac{2}{3}}

a)

$10$

b)

$\frac{1}{25}$

c)

$250$

d)

$\frac{1}{5}$

40.

Simplify without a calculator:

\left(2\right)^{10}

a)

$1024$

b)

$256$

c)

$64$

d)

$128$

41.

Simplify without a calculator:

\left(2\right)^8

a)

$1024$

b)

$256$

c)

$64$

d)

$128$

42.

Simplify without a calculator:

\left(2\right)^5

a)

$1024$

b)

$256$

c)

$64$

d)

$32$

43.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

44.

Change $\log_5⁡7$ into the form of $\frac{\log_3⁡a}{\log_3⁡b}$ , where $a$ and $b$ are integers

a)

$\frac{\log_3⁡5}{\log_3⁡7}$

b)

$\frac{\log_3⁡7}{\log_3⁡5}$

45.

Change $\log_{12}⁡2$ into the form of $\frac{\log_5⁡a}{\log_5b}$ , where $a$ and $b$ are integers

a)

$\frac{\log_512}{\log_52}$

b)

$\frac{\log_5⁡2}{\log_5⁡12}$

46.

Change $\log_5⁡7$ into the form of $\frac{\log⁡a}{\log⁡b}$ , where $a$ and $b$ are integers

a)

$\frac{\log⁡5}{\log⁡7}$

b)

$\frac{\log⁡7}{\log⁡5}$

47.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

48.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

49.

Solve for x:
log_xe=1

a)

1

b)

e

c)

0

d)

No solution

50.

Solve for x:
e^x=7

a)

x=ln7

b)

x=ln⁷

c)

x=7^ln

d)

No solution

7.4 Precal log and exp exam

Total questions: 50

Worksheet time: 4hrs 10mins

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