Question

8^x = 16 then x = ______.

Options

• 2

• 4

• `3/4`

• `4/3`

Answer 1

8^x = 16 then x = `underlinebb(4/3)`.

Explanation:

Step-by-step:

The given equation is 8^x = 16.

Both sides of the equation are expressed with a common base, which is 2.

The number 8 is rewritten as 2³.

The number 16 is rewritten as 2⁴.

Substituting these into the equation, it becomes (2³)^x = 2⁴.

Using the power of a power rule, (a^m)ⁿ = a^mn, the left side is simplified to 2^3x. 

The equation now is 2^3x = 2⁴.

Since the bases are equal, the exponents are equated: 3x = 4.

To solve for x, both sides of the equation are divided by 3.

The value of x is found to be `4/3`.