Question

Wendy is looking over some data regarding the strength, measured in Pascals (Pa), of some rope and how the strength relates to the number of woven strands in the rope. The data are represented by the exponential function f(x) = 2x, where x is the number of woven strands. Explain how she can convert this equation to a logarithmic function when strength is 256 Pascals.

Answer 1

$f(x)= 2^{x}$

When strength f(x) = 256, we can write:

$256= 2^{x}$

In order to convert it to logarithm, take log of both sides to the base 2. The equation becomes:

$log_{2}(256)= log_{2}(2^{x} )$

Using the power property of log, we can write:

$log_{2}(256)= x*log_{2}(2) \\ \\ log_{2}(256)= x$

The above expression has been converted to logarithmic form.