Question

If 5 + 20 times 2 Superscript 2 minus 3 x Baseline = 10 times 2 Superscript negative 2 x Baseline + 5, what is the value of x?

Answer 1

the answer is 3

Explanation:

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Answer 2

x=3

Explanation:

We want to solve the equation:

`5 + 20 * {2}^(2 - 3x) = 10 * {2}^( - 2x) + 5`

We subtract 5 from both sides to get:

`20 * {2}^(2 - 3x) = 10 * {2}^( - 2x)`

We divide both sides by 10 to get:

`2 * {2}^(2 - 3x) = {2}^( - 2x)`

`{2}^(1) * {2}^(2 - 3x) = {2}^( - 2x)`

We now simplify LHS using the product rule:

`{2}^(1 + 2 - 3x) = {2}^( - 2x)`

Since the base is the same on both sides, we equate the exponents to get:

`1 + 2 - 3x = - 2x`

`1 + 2 = - 2x + 3x`

`x = 3`