Free Printable Precal 7.1 exponents and logarithms mental math

1.

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

a)

$3$

b)

$\frac{2}{3}$

c)

$27$

d)

$\frac{1}{3}$

2.

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

a)

$4$

b)

$-3$

c)

$-2$

d)

$-4$

3.

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

a)

$2$

b)

$\frac{1}{2}$

c)

$-\frac{1}{2}$

d)

$-2$

4.

$Evaluate\ \ \ \ \ \log_{10}\ 1,000,000$

a)

$1$

b)

$\frac{1}{6}$

c)

$100$

d)

$6$

5.

$Evaluate\ \ \ \ \ \log_2256$

a)

$2$

b)

$4$

c)

$8$

d)

$6$

6.

$Evaluate\ \ \log_39$

a)

$2$

b)

$\frac{1}{2}$

c)

$\frac{1}{3}$

d)

$3$

7.

$Evaluate\ \ \log_93$

a)

$2$

b)

$\frac{1}{2}$

c)

$\frac{1}{3}$

d)

$3$

8.

$Evaluate\ \ \log_327$

a)

$2$

b)

$\frac{1}{2}$

c)

$\frac{1}{3}$

d)

$3$

9.

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

a)

$\frac{1}{3}$

b)

$-\frac{1}{2}$

c)

$-1$

d)

$3$

10.

$Evaluate\ \ \log_3\left(\frac{1}{9}\right)$

a)

$-2$

b)

$-\frac{1}{2}$

c)

$-1$

d)

$3$

11.

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

a)

$-2$

b)

$-\frac{1}{2}$

c)

$-1$

d)

$3$

12.

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

a)

$-2$

b)

$-\frac{1}{2}$

c)

$0$

d)

$3$

13.

$Evaluate\ \ \log_3\left(3\right)$

a)

$-2$

b)

$-\frac{1}{2}$

c)

$0$

d)

$1$

14.

$Evaluate\ \ \log_3\left(3^4\right)$

a)

$4$

b)

$2$

c)

$0$

d)

$3$

15.

$Evaluate\ \ \log_3\left(\frac{1}{3^4}\right)$

a)

$4$

b)

$2$

c)

$-4$

d)

$-3$

16.

$Evaluate\ \ \log_2\left(2^{\frac{1}{3}}\right)$

a)

$4$

b)

$\frac{1}{2}$

c)

$-4$

d)

$\frac{1}{3}$

17.

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

a)

$4$

b)

$\frac{1}{2}$

c)

$2$

d)

$\frac{1}{3}$

18.

$Evaluate\ \ \log_2\left(8\right)$

a)

$4$

b)

$\frac{1}{2}$

c)

$2$

d)

$3$

19.

$Evaluate\ \ \log_2\left(16\right)$

a)

$4$

b)

$\frac{1}{2}$

c)

$2$

d)

$3$

20.

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

a)

$8$

b)

$6$

c)

$7$

d)

$3$

21.

$Evaluate\ \ \log_2\left(\frac{1}{8}\right)$

a)

$-1$

b)

$-2$

c)

$-4$

d)

$-3$

22.

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

a)

$-1$

b)

$-2$

c)

$-4$

d)

$-3$

23.

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

a)

$e$

b)

$2$

c)

$1$

d)

$\frac{1}{2}$

24.

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

a)

$e$

b)

$2$

c)

$1$

d)

$\frac{1}{2}$

25.

$Evaluate\ \ \ln\left(\frac{1}{\sqrt{e}}\right)$

a)

$e$

b)

$\frac{1}{2}$

c)

$1$

d)

$-\frac{1}{2}$

26.

$Evaluate\ \ \ln\left(\frac{1}{e^{-5}}\right)$

a)

$e$

b)

$-5$

c)

$5$

d)

$-\frac{1}{2}$

27.

Simplify without a calculator:

4^{-1}

a)

$\frac{1}{2}$

b)

$4$

c)

$2$

d)

$\frac{1}{4}$

28.

Simplify without a calculator:

4^{-2}

a)

$\frac{1}{16}$

b)

$8$

c)

$16$

d)

$\frac{1}{8}$

29.

Simplify without a calculator:

4^{-3}

a)

$\frac{1}{16}$

b)

$\frac{1}{64}$

c)

$64$

d)

$\frac{1}{8}$

30.

Simplify without a calculator:

4^0

a)

$4$

b)

$0$

c)

$1$

d)

$\frac{1}{4}$

31.

Simplify without a calculator:

\left(\frac{3}{5}\right)^{-2}

a)

$\frac{3}{5}$

b)

$\frac{25}{9}$

c)

$\frac{9}{25}$

d)

$\frac{5}{3}$

32.

Simplify without a calculator:

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

a)

$\frac{8}{27}$

b)

$\frac{9}{4}$

c)

$\frac{8}{25}$

d)

$\frac{27}{8}$

33.

Simplify without a calculator:

\left(\frac{2}{3}\right)^0

a)

$\frac{3}{2}$

b)

$0$

c)

$1$

d)

$\frac{2}{3}$

34.

Simplify without a calculator:

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

a)

$10$

b)

$10,000$

c)

$1$

d)

$\frac{1}{10}$

35.

Simplify without a calculator:

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

a)

$10$

b)

$10,000$

c)

$1000$

d)

$100,000$

36.

Simplify without a calculator:

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

a)

$\frac{1}{1000}$

b)

$\frac{1}{30}$

c)

$1000$

d)

$\frac{1}{10}$

37.

Simplify without a calculator:

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

a)

$\frac{1}{1000}$

b)

$\frac{1}{30}$

c)

$1000$

d)

$\frac{1}{10}$

38.

Simplify without a calculator:

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

a)

$10$

b)

$5$

c)

$250$

d)

$25$

39.

Simplify without a calculator:

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

a)

$10$

b)

$5$

c)

$250$

d)

$25$

40.

Simplify without a calculator:

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

a)

$10$

b)

$\frac{1}{25}$

c)

$250$

d)

$\frac{1}{5}$

41.

Simplify without a calculator:

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

a)

$10$

b)

$\frac{1}{25}$

c)

$250$

d)

$\frac{1}{5}$

42.

Simplify without a calculator:

\left(\frac{1}{25}\right)^{\frac{1}{2}}

a)

$5$

b)

$\frac{1}{25}$

c)

$250$

d)

$\frac{1}{5}$

43.

Simplify without a calculator:

\left(\frac{1}{25}\right)^{-\frac{1}{2}}

a)

$5$

b)

$\frac{1}{25}$

c)

$250$

d)

$\frac{1}{5}$

44.

Simplify without a calculator:

\left(\frac{1}{25}\right)^{-\frac{3}{2}}

a)

$5$

b)

$\frac{1}{125}$

c)

$125$

d)

$\frac{1}{5}$

45.

Simplify without a calculator:

\left(\frac{1}{25}\right)^{\frac{3}{2}}

a)

$5$

b)

$\frac{1}{125}$

c)

$125$

d)

$\frac{1}{5}$

46.

Simplify without a calculator:

\left(\frac{1}{27}\right)^{\frac{4}{3}}

a)

$81$

b)

$\frac{1}{81}$

c)

$9$

d)

$\frac{1}{9}$

47.

Simplify without a calculator:

\left(\frac{1}{27}\right)^{-\frac{4}{3}}

a)

$81$

b)

$\frac{1}{81}$

c)

$9$

d)

$\frac{1}{9}$

48.

Simplify without a calculator:

\left(\frac{9}{64}\right)^{\frac{1}{2}}

a)

$81$

b)

$\frac{3}{8}$

c)

$8$

d)

$\frac{2}{9}$

49.

Simplify without a calculator:

\left(\frac{16}{81}\right)^{\frac{3}{4}}

a)

$81$

b)

$\frac{4}{9}$

c)

$\frac{27}{8}$

d)

$\frac{8}{27}$

50.

Simplify without a calculator:

\left(2\right)^{10}

a)

$1024$

b)

$256$

c)

$64$

d)

$128$

Precal 7.1 exponents and logarithms mental math

Total questions: 50

Worksheet time: 33mins

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