A cube of side length 2 m is composed of two materials, separated by a plane slanting down from the top corner to cut the bottom face in a diagonal, as in the figure shown below. The material below the plane has density P gm/m3 and the material above the plane has density Q gm/m3.(a) Find the mass of the portion of the cube below the slanted plane. Your answer will be in terms of P. This is an upper case P.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places