Question

PLEASE HELP 30 POINTS 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) = 2x, where x is the length. Explain how he can convert this equation to a logarithmic function when strength is 8 Pascals.

Answer 1

Logarithmic functions and exponential functions are inverse and opposite of one another

The logarithmic function is $y = \log_2(x)$, and the length at 8 pascals is 3 units

How to determine the logarithmic function

The exponential function is given as:

$f(x) = 2^x$

Express f(x) as y

$y = 2^x$

Swap the positions of x and y

$x = 2^y$

Take the logarithm of both sides

$\log(x) = \log(2^y)$

Apply the rule of logarithm

$\log(x) = y\log(2)$

Divide both sides by log(2)

$y = \frac{\log(x)}{\log(2)}$

Apply the change of base rule of logarithm

$y = \log_2(x)$

When the strength is 8 pascals, we have:

$y = \log_2(8)$

Express 8 as 2^3

$y = \log_2(2^3)$

So, we have:

$y =3 \log_2(2)$

Evaluate log 2 base 2

$y =3$

Hence, the logarithmic function is $y = \log_2(x)$, and the length at 8 pascals is 3 units

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