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Exponent Laws

100

Simplify:

3^4  x   3^2

Ans

3^6

200

Rewrite with a positive exponent:

x^-3

Ans:

1/x^3

300

Simplify:

(5^3)^2

Ans:

5^6

400

Simplify:

(2^7) / (2^3)

Ans:

2^4     =      16

500

Write as a single Power:

4^3   x    8^2

Ans:

(2^2)^3   (2^3)^2

= 2^(6 + 6)

= 2^12

Log Laws

100

Evaluate:

log(1000)

Ans:

3

200

Expand:

log(5x)

Ans:

log(5)  + log(x)

300

Condense:

log(x) + 2log(y)

Ans:

log(xy^2)

400

Rewrite using change of base:

log base 3 x (10)

Ans:

log(10) / log(3)

500

Simplify:

log [(a^3)/(b^1/2)]

Ans:

3log(a) - 1/2 log(b)

Solve Exp Equations

100

Solve:

2^x = 8

Ans:

x = 3

200

Solve:

5^(x+1) = 25

Ans:

x = 1

300

Solve:

7^x = 4

Ans:

x = log4 / log7

400

Solve:

3^2x = 27

Ans:

x = 3/2

500

Solve:

4^x+1 = 10

Ans:

x = log base 4 (10) - 1

Solve Log Equations

100

Solve:

log base 2 (x) = 5

Ans:

x = 32

200

solve:

log(x) + log(2) = 3

Ans:

x = 500

300

Solve:

log base 5 (2x - 1) = 2

Ans:

x = 13

400

Solve:

log(x) - log(x-3) = 1

Ans:

x = 10/3

500

Solve:

log(x+4) = 2

Ans:

e^2 - 4

Word Problems

100

A bacteria pop doubles every hr. if there are 200 bacteria now, how many in 3 hrs?

200(2^3) = 1600

200

rewrite in exp form:

log base 5 (125) = 3 

Ans:

5^3 = 125

300

Solve for time:

A = 500e^(0.12t)

Find t when A = 800

^Ans:

^{800 = 500e^(0.12)}

^{t = log(1.6)/0.12}

400

T(t) = 22 + (68)e^(-1.5t)

Find Temp at t = 10

Ans:

22 + 68e^(-1.5)

500

Radioactive decay:

A substance has a half life of 12 years. Write an equation for the amount remaining from an initial 80 grams.

Ans:

A(t) = 80 (1/2)^(t/12)