Asmall cube and a large cube with edge lengths represented by expressions are shown in the diagram below.
x inches 3x inches
the small cube has a volume of 64 cubic inches.
a. what is the value of x? show or explain how you got your answer.
b. what is the surface area, in square inches, of the small cube? show or explain how you got your answer.
c. the surface area of the large cube is how many times the surface area of the small cube? show or explain how you got your answer.
d. the volume of the large cube is how many times the volume of the small cube? show or explain how you got your answer.

the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point

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