Question

Обчисліть log 3 4×log5 7×log7 81​

Answer 1

ОТВЕТ ВО ВЛОЖЕНИИИИИИИИИИ

Answer 2

To calculate the value of the expression "log₃(4) × log₅(7) × log₇(81)," we can use the property of logarithms that states:

logₐ(b) = logₓ(b) / logₓ(a)

where logₐ(b) is the logarithm of b to the base a, and logₓ is the natural logarithm.

Now, let's calculate each part step by step:

1. log₃(4) = logₓ(4) / logₓ(3) Since the base x is not specified, we can use the natural logarithm, denoted as "ln": logₓ(4) = ln(4) and logₓ(3) = ln(3) Therefore, log₃(4) = ln(4) / ln(3).

2. log₅(7) = logₓ(7) / logₓ(5) logₓ(7) = ln(7) and logₓ(5) = ln(5) Therefore, log₅(7) = ln(7) / ln(5).

3. log₇(81) = logₓ(81) / logₓ(7) logₓ(81) = ln(81) and logₓ(7) = ln(7) Therefore, log₇(81) = ln(81) / ln(7).

Now, let's multiply all these parts together:

log₃(4) × log₅(7) × log₇(81) = (ln(4) / ln(3)) × (ln(7) / ln(5)) × (ln(81) / ln(7))

Notice that ln(7) appears both in the numerator and denominator. We can cancel it out:

log₃(4) × log₅(7) × log₇(81) = (ln(4) / ln(3)) × (ln(81) / ln(5))

Now, we can simplify further:

log₃(4) × log₅(7) × log₇(81) = ln(4) × ln(81) / (ln(3) × ln(5))

Finally, we can use the property of logarithms that logₐ(b) × logₐ(c) = logₐ(b^c):

log₃(4) × log₅(7) × log₇(81) = ln(4^ln(81)) / ln(3) = ln(4^4) / ln(3) = ln(256) / ln(3)

To obtain a numeric approximation, we can calculate this using a calculator:

log₃(4) × log₅(7) × log₇(81) ≈ 5.54517796238 / 1.09861228867 ≈ 5.0528

So, the value of the expression is approximately 5.0528.