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?

Question

asked Oct 17, 2021 2.8k views

2 Answers

Drgmak · Answer 1 · 2021-10-21T16:41:02+0000

Answer:

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