- 12

- 0

a) log (4) 16 = 2 ans: 16 = 4^2

b) log (16) 2 = 1/4 ans: 2 = 16^1/4

c) log (2) 1/16 = -4 ans: 1/16 = 2^-4

d) 2^5 = 32 how do you express in log form? ans: 5 = log (2) 32

e) 36^1/2 = 6 ans: 1/2 = log (36) 6

f) 4^-4 = 1/81 ans: -4 = log (3) [1/81]

g) log (3) 81 =? ans: 4

h) log (2) 1/64 ? ans: -6

i) log (3) (27)^1/2 ans: 3/2

j) log (1/2) 4 ans: -2

k) log(10) 5 - log (10) 50 ans: -1

l) log (6) 18 + log (6) 12 ans: 3

how do you conve\rt to exponential form and solve for x?

a) log (2) 5x = 7 ans: 128/5

b) log (10) x^3 = 18 ans: 10^6

c) 2log (4) [8x] = 5 ans: 4

d) log(5) [3x^2] - log(5) [15x] = 3 ans: 625

e) log (x) 64 = 3/2 ans: 16

Which is larger?

a) 2log5 or 3log3 ans: 3 log 3

b) 1/2 log(2) 16 or 1/3 log (3) 27? ans: 1/2 log (2) 16

HOw do you solve for x:

a) 10^5x = 25 ans: 1/5 log 25 = 0.279

b) 2^x = 1000 ans: 3/log 2 = 9.965

c) 4^2x = 200 ans: log 200/log 16 = 1.9109

9) magnitudes of earthquatkes are measured by using the richeter scale. on thisscale, the

magnitude R of an earthquake is given by R = log (10)[I/I (subscript 0)]

wher I is the intensity of the earthquake being measured and I 0 is a fixed standanrd

intensity used for comparison.

a) show that if an earthquake measures R = 4 on the richter scale, then its intensity is 10

000 times teh standard.

b) how many times morei intense is an earthquake measuring R = 6 than one measruing R = 4?

ans: 100 times more intense

c) the mexico city eartquake of 1985 measured 8.1 on the richeter scale. express its

intensity in terms of the standard intensity.

ans:1.26 x 10^8 Io