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

Log base 2 (strength) = x. When the strength is 256 Pa to get -> log base 2 strength 256 = x. To get 8.

I recently had this question as well. And literally just now found this http://www.miniwebtool.com/log-base-2-calculator/

Hopefully, it helps in the future :)

Answer 2

Answer:

Taking logarithm on both sides with base 2, she can convert the equation to a logarithmic function to get the solution x = 8.

Step-by-step explanation:

We are given that,

The function representing the strength of the rope in Pascals is given by,

$f(x)=2^x$

Now, the strength is given to be 256 Pascals i.e. $f(x)=256$.

So, the relation becomes, $256=2^x$

As, we know, $y=b^x$ can be converted by taking 'log with base b' to $\log_b y= x\log_b b$.

Taking logarithm with base 2 on both sides, we get,

$\log_2 256=x\log_2 2$

i.e. $x=\frac{\log_2 256}{\log_2 2}$

i.e. $x=\frac{2.408}{0.301}$

i.e. x = 8

Thus, taking logarithm on both sides with base 2, she can convert the equation to a logarithmic function.