Which equation is equivalent to (1/3)^x = 27 ^x + 2

Explanation:

We have been given with the expression

Now, to solve the equation firstly we have to make the base same on both sides

27 can be written as

Hence, given expression can be rewritten as

Now since, base is same we can equate the powers on both sides

Therefore given expression is equivalent to

Equivalent means the simplified form of any given expression

To find the equivalent expression, we need to expand the given expression by using  law of indices.

The equation is equivalent to .

Given:

The given equation is .

Solving left hand side of the equation.

Apply the law of indices.

Solving right hand side of the equation.

Thus, the equation is equivalent to .

Learn more about law of indices here:

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step-by-step explanation:

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.