Hence the value for x given the strength is 116 Pascals is 6.8571
From the question given, we are told that the 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 is expressed as;
[tex]f(x)=2^x[/tex]
let y = f(x), hence;
[tex]y = 2^x[/tex]
Since the base number is 2, we can proceed to take the logarithm to base 2 of both sides as shown;
[tex]log_2 y = log_2 2^x\\log_2 y = xlog_2 2\\[/tex]
Since log₂2 = 1, then;
[tex]log_2 y = x\\Swap\\x=log_2 y[/tex]
Given that the strength is 116, then y = 116
[tex]x=log_2 116\\[/tex]
This can also be expressed as:
[tex]x=\frac{log_{10} 116}{log_{10} 2}[/tex]
[tex]x=\frac{2.064}{0.3010} \\x=6.8571[/tex]
Hence the value for x given the strength is 116 Pascals is 6.8571
Learn more here on logarithm here: https://brainly.com/question/12983107
