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

Answer:

x=3

Step-by-step explanation:

We want to solve the equation:

$5 + 20 \times {2}^{2 - 3x} = 10 \times {2}^{ - 2x} + 5$

We subtract 5 from both sides to get:

$20 \times {2}^{2 - 3x} = 10 \times {2}^{ - 2x}$

We divide both sides by 10 to get:

$2 \times {2}^{2 - 3x} = {2}^{ - 2x}$

${2}^{1} \times {2}^{2 - 3x} = {2}^{ - 2x}$

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:

$1 + 2 - 3x = - 2x$

$1 + 2 = - 2x + 3x$

$x = 3$