# Another calculus problems

how do you express in exponential form?
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

Tom Mattson
Staff Emeritus
Gold Member
We are happy to help you with your homework, but we don't want to do it for you. Besides, these problems aren't that difficult.

Have you tried them? Can you show us how you started?

Do that, and we will help through the rough spots.

yes
this is a very easy question
i suggest you read the book