The exponential function g(x) = 2x represents the strength of a rope due to its length. Let g(x) represent the strength of the rope measured in Pascals, and let x represent the length of the rope in meters. Part A: Convert the exponential function to a logarithmic function. Be sure to show/explain all steps to receive full credit. Part B: Determine the length of a rope when the strength is 8 Pascals. (That is find x when g(x) = 8). Be sure to show all work to receive full credit.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

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