Question

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Answer 1

Step-by-step explanation:

1) Given:

$\frac{ {2}^{2x - 1} }{ {2}^{x + 2} } = 4$

To find: Solve for x

Solution:

Use law of exponents

$\boxed{\bold{ {x}^{a} \times {x}^{b} = {x}^{a + b} }}\\ \\ \boxed{\bold{\frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} }}$

$\frac{ {2}^{2x - 1} }{ {2}^{x + 2} } = 4 \\ \\ {2}^{2x - 1 - x - 2} = 4 \\ \\ {2}^{x - 3} = 4 \\ \\{2}^{x - 3} = {2}^{2}$

compare the power

$x - 3 = 2 \\ \\ x = 2 + 3 \\ \\ \bold{\red{x = 5 }}$

2) Given:

$\frac{ {5}^{5} \times {5}^{ - 4} \times {5}^{x} }{ {5}^{12} } = {5}^{ - 5}$

To find: Value of x

Solution:

$\frac{ {5}^{5} \times {5}^{ - 4} \times {5}^{x} }{ {5}^{12} } = {5}^{ - 5} \\ \\ {5}^{5 - 4 + x - 12} = {5}^{ - 5} \\ \\ {5}^{x - 11} = {5}^{ - 5}$

compare powers

$x - 11 = - 5 \\ \\ x = - 5 + 11 \\ \\ \bold{\green{x = 6}}$

Final answer:

1) x= 5

2) x= 6

Hope it helps you.

To learn more on brainly:

solve this problem 5+5^2×5^-1

https://brainly.in/question/42860713