Question

Log0,8(5)*log5(1,25)

Answer 1

Смотри.......................

Answer 2

To calculate the value of the expression log₀.₈(5) * log₅(1.25), we can use the change of base formula for logarithms. The change of base formula states that logₐ(b) = logₓ(b) / logₓ(a), where x can be any base.

Let's calculate each logarithm separately and then multiply the results:

1. Calculating log₀.₈(5): We can rewrite log₀.₈(5) using the change of base formula: log₀.₈(5) = logₓ(5) / logₓ(0.8)

We can choose any base x for the logarithms. Let's choose x = 10 for simplicity: logₓ(5) / logₓ(0.8) = log₁₀(5) / log₁₀(0.8)

Using a calculator, we find that log₁₀(5) ≈ 0.69897 and log₁₀(0.8) ≈ -0.09691:

log₁₀(5) / log₁₀(0.8) ≈ 0.69897 / -0.09691 ≈ -7.202

2. Calculating log₅(1.25): Using the base 10 logarithm, we have: log₅(1.25) = log₁₀(1.25) / log₁₀(5)

Using a calculator, we find that log₁₀(1.25) ≈ 0.09691:

log₁₀(1.25) / log₁₀(5) ≈ 0.09691 / 0.69897 ≈ 0.139

Now, we can multiply the results of the two logarithms: -7.202 * 0.139 ≈ -0.999

Therefore, log₀.₈(5) * log₅(1.25) ≈ -0.999.