Question

Log4 (7) - log4 (2/7) + log4 (1/8)

Answer 1

Ответ:

Пошаговое объяснение:

Решение дано на фото.Всё подробно написала.

Answer 2

To simplify the expression log₄(7) - log₄(2/7) + log₄(1/8), you can use logarithm properties.

1. Recall the properties of logarithms:

   • logₐ(b) - logₐ(c) = logₐ(b/c)
   • logₐ(b) + logₐ(c) = logₐ(b * c)

2. Apply these properties to your expression:

log₄(7) - log₄(2/7) + log₄(1/8)

= log₄(7) + log₄(7/2) + log₄(1/8)

3. Use the product rule for logarithms:

log₄(7 * 7/2 * 1/8)

4. Simplify the expression inside the logarithm:

= log₄(49/16)

5. You can further simplify this by finding the square root of 49 and the square root of 16:

= log₄(7²/4²)

= log₄((7/4)²)

6. Finally, apply the power rule of logarithms:

= 2 * log₄(7/4)

So, the simplified expression is 2 * log₄(7/4).