Question

1) x^12 = 5 2) x^11 = 7

Answer 1

Ответ:

Завдання розв'язано..

Answer 2

To solve these equations, you can use logarithms. You want to isolate "x" in each equation. Here's how you can do it:

1. x^12 = 5

Take the logarithm of both sides. You can use any base for the logarithm, but commonly used bases are natural logarithm (ln) and base 10 logarithm (log):

ln(x^12) = ln(5)

Apply the logarithm rule that allows you to bring the exponent down in front:

12 * ln(x) = ln(5)

Now, isolate ln(x) by dividing both sides by 12:

ln(x) = ln(5) / 12

To solve for "x," you can exponentiate both sides with the base "e" (since you used the natural logarithm, which has base "e"):

x = e^(ln(5) / 12)

x is approximately equal to:

x ≈ 1.0801

2. x^11 = 7

Follow a similar procedure:

ln(x^11) = ln(7)

Use the logarithm rule to bring the exponent down:

11 * ln(x) = ln(7)

Isolate ln(x) by dividing both sides by 11:

ln(x) = ln(7) / 11

To solve for "x," exponentiate both sides with the base "e":

x = e^(ln(7) / 11)

x is approximately equal to:

x ≈ 1.1604