Question

Assume that x, y, z and b are positive numbers. Use the properties of logarithms to write the expression logb 4(square root)x^7y^2 / z^4 in terms of the logarithms of x, y and z

a. 28logbx+8logby-16logbz
b. 7/4 logbx+1/2 logby-logbz
c. 7/4logb(x+y-z)
d. logb x+1/2 logby-logbz
e. 7/4 logbx + logby-logbz

I am not sure how to work this out so if you could help me to work through the question I would really appreciate it. Thank you!

Answer 1

What are the properties of logarithms? Do you know?

Answer 2

http://www.google.com/#q=properties+of+logarithms

Answer 3

I've just looked at the link Ms. Sue posted so now I know them and have written them down in my notebook so I remember them

Answer 4

I'm still struggling to figure out the answer though. Ms. Sue can you help me?

Answer 5

I have this same question. I've looked at the link too and can't figure it out. Miriam what did you get?

Answer 6

Assuming all logs are base b (since the base does not matter for this kind of stuff), we have (I think)

log ∜(x^7 y^2 / z^4)
= 1/4 log(x^7 y^2 / z^4)
= 1/4 (7logx + 2logy - 4logz)
= 7/4 logx + 1/2 logy - logz

or, (b)