Question

Please help I really don't understand this 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) = 2^x, 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

@Hero @dan815 Please help... I don't want the flat out answer but I have no idea where to begin and the lessons FLVS provide aren't helpful.

Answer 2

the number of woven strands in the rope. The data are represented by the exponential function f(x) = 2x


-----------
2x is not exponential.
It's linear.

Answer 3

remember

\[\huge \log_{b} y = x~~~or~~~b^x=y\]

Answer 4

you have
\[\huge 256 = 2^x\]

Answer 5

Thank you!! So 256 is just substituted in for f(x)?

Answer 6

yes, f(x) is a strength [Pa] as a function of strans [x]

Answer 7

and so, 256=2^8?

Answer 8

I'm stuck on the " Explain how she can convert this equation to a logarithmic function"

Answer 9

they just want it as a log function, take log base 2 of both sides

f(x) = 2^x

\[\huge \log_{2}f(x) = \log_{2}2^x \]

\[\huge \log_{2}f(x) = x*\log_{2}2 = x*1 \]
\[\huge \log_{2}f(x) = x \]

Answer 10

if you put 256 in for f(x), you can get a number of strands x required for that strength

Answer 11

ok, so it's essentially the same numbers we worked out before, just with the logs stuck in?

Answer 12

yeah a log is the inverse of the exponential, just changed it around

Answer 13

logarithms are nothing more than exponents

Answer 14

Thank you so so much!!

Answer 15

welcome