Converting exponential functions to logarithmic form?

Question

How do I go about converting an exponential function like y=100(2.24)^x to logarithmic form? What is the general rule?Thank you so much!

Answer 1

y = 100(2.24)^x

Take the log (common logarithm of base 10) of both sides.

General rules:

m*n = log m + log n
m/n = log m - log n
m^a = a(log m)

log (y) = log(100) + x log (2.24)

The logarithm of 100 is 2

log (y) = 2 + x log (2.24)

log of 2.24 = 0.35

log (y) = 2 + 0.35x

We could have used natural logarithms (base of e)
.

Answer 2

First get the exponential part alone:
y/100 = 2.24^x

To convert from exponential to logarithmic form remeber two things: base goes to base, what the log is equal to is the expoenent.
So in general y = b^x becomes x = log(base b) x.

So converting the expression above:
x = log (base 2.24) (y/100)

Answer 3

Here's another approach.
Basic principle:   m = b^n as a log is n = log[b]m

Process...
First, get the exponential part by itself.
   y/100 = (2.24)^x

Next, rewrite as a log equation.
   The base of the log is always the same as the base of the exponent.
   The log [by definition] is always equal to the exponent.
   Take the log of what ever the exponent part equals. [In this case the exponent part equals y/100]

SO, your prob...
   log[2.24] (y/100) = x   [ log base 2.24 of (y/100) = x ]