Algebra help

Question

Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x) = 2^x, where x is the length. Explain how he can convert this equation to a logarithmic function when strength is 8 Pascals.

Answer 1

Hi, Jessica!

The key to this problem is to convert our exponential function into a logarithmic one.

In general, we can covert from exponential functions to logarithmic functions using the following method:

a^b = c --> log_a(c) = b

Our original formula is f(x) = 2^x, where f(x) represents strength, and x represents length. We are given a strength of 8 Pascals, so we can plug this into our exponential equation by noting that f(x) = 8:

f(x) = 2^x = 8

We can then use the general exponential to logarithmic conversion above, where in our example, a = 2, b = x, and c = 8:

2^x = 8 --> log₂(8) = x

This logarithmic equation shows how to calculate the length when the strength is 8 Pascals.

I hope that this explanation was helpful, and please don't hesitate to reach out if you have any further questions!