Expert: Paul Klarreich - 12/17/2007

Question
Logarithmic Having trouble understanding how to. on a couple of problems. solve Log littlex 64=3    and simplify log little 1/5 25
thanks

Answer
Questioner:   Bunny
Category:  Advanced Math
Private:  No
 
Subject:  Math 108
Question:  Logarithmic Having trouble understanding how to. on a couple of problems. solve Log littlex 64=3    and simplify log little 1/5 25
thanks
............................................
Hi, Bunny,

The 'log' notation is hard to send through this site, so I will have to guess at what you are trying to say.

1. solve Log littlex 64=3

I think you mean here, that x is the base of the logarithm.  YOu can write:

log[x](64) = 3

-- put the base in [], the argument in ()  next time.

Now the principle is that logs and exponentials are inverses.  So:

log[b](x) = y

means

b^y = x

So
log[x](64) = 3
means

x^3 = 64

and that gives you x = 4.

2.log little 1/5 25

that is:

log[1/5](25)

Okay, give that a name, like y.

log[1/5](25) = y

means

(1/5)^y = 25

Now do some exponent stuff:

1/5 = 5^-1, and  25 = 5^2.  (Convenient, that we can use 5 both times.  In fact, we have to.)

(5^-1)^y = 5^2

5^-y = 5^2

-y = 2,

y = -2.
That's your answer.