Logs And Exponents

Name: ___________________________

Lomas MB43

Logarithms and Exponents Review (due Monday) 1.

The function y = 2 is equivalent to x

(1) x = y log 2 (2) x = log 2 y

2.

What is the value of 2 −3 ?

4.

Find x to the nearest tenth. 5x = 3.6

(3) y = x log 2 (4) y = log 2 x

3.

If log x 9 = −2, what is the value of x?

5.

If log a = 2 and log b = 3, what is the numerical value 6. of log (1) 8 (2) –8

a b

3

?

If log a = x and log b = y , what is log a b ? (1) x + 2 y

(3) 25 (4) –25

(2) 2 x + 2 y

x+y 2 y (4) x + 2 (3)

7.

Find x: log x 4 + log x 9 = 2,

8.

Write in exponential form. 1.5 = log4 8

9.

Write in logarithmic form. 7² = 49

10 .

Find the value of x. log9 3 = x

11 .

Solve algebraically for x: 8 2 x = 4 6

12 .

Find the value of x. log6 X = 2

13 .

Solve for x: log b 36 − log b 2 = log b x

14 .

Solve for x to the nearest hundredth. log35 + log3x = log3(7 + x)

15 .

Solve for x: logb 3 + logb x = logb 12

16 .

Solve for m: 3m+1 − 5 = 22

17 .

The number of houses in Central Village, New York, 18 grows every year according to the function . H(t ) = 540(1039 . ) t , where H represents the number of houses, and t represents the number of years since January 1995. A civil engineering firm has suggested that a new, larger well must be built by the village to supply its water when the number of houses exceeds 1,000. During which year will this first happen?

A population of wolves in a county is represented by the equation P(t ) = 80(0.98) t , where t is the number of years since 1998. Predict the number of wolves in the population in the year 2008.