Question

4 ^ x - 4 ^ 0 - 255 = 0​

Answer 1

x = 4

Explanation:

Given the equation:

`\displaystyle{4^x - 4^0 - 255=0}`

We know that
`\displaystyle{a^0 = 1}` where a ≠ 0. Therefore,

`\displaystyle{4^x - 1 - 255=0}\\\\\displaystyle{4^x - 256=0}`

Add both sides by 256, so we have:

`\displaystyle{4^x=256}`

Factor 256 out:

256 = 2 x 128 = 2 x 2 x 2⁶ = 2⁸

Therefore, 256 = 2⁸.

`\displaystyle{4^x=2^8}`

Convert to the same base:

`\displaystyle{\left(2^2\right)^x=2^8}\\\\\displaystyle{2^(2x) = 2^8}`

When two sides have same base, solve the equation through exponents:

`\displaystyle{2x=8}`

Divide both sides by 2, so we have:

`\displaystyle{x=4}`