Question

Log 0,2 8- log 0,2 200

Answer 1

$log_{0,2}8-log_{0,2} 200=log_{0,2}\frac{8}{200}=log_{0,2}\frac{1}{25} =log_{0,2}0,04=log_{0,2} 0,2^{2} =2log_{0,2}0,2=2\\\\Otvet:\boxed{2}$

Answer 2

Воспользуемся свойством частного логарифмов

log 0,2 8- log 0,2 200＝log 0.2 (8/200)＝log 0.2 0.04＝2

Answer 3

To evaluate the expression log₀,₂8 - log₀,₂200, we can use the logarithmic property which states that:

logₐb - logₐc = logₐ(b/c)

Applying this property, we have:

log₀,₂8 - log₀,₂200 = log₀,₂(8/200)

Now, let's simplify the fraction:

8/200 = 1/25 = 1/₅²

Using the property that logₐaⁿ = n * logₐa, we can rewrite the expression as:

log₀,₂(1/₅²) = -2 * log₀,₂₅

Now, we need to convert the base 2 logarithm to a base 10 logarithm using the change of base formula:

log₀,₂x = log₁₀x / log₁₀2

Therefore,

-2 * log₀,₂₅ = -2 * (log₁₀25 / log₁₀2)

Using a calculator, we can find that log₁₀25 ≈ 1.39794 and log₁₀2 ≈ 0.30103:

-2 * (1.39794 / 0.30103) ≈ -2 * 4.64159 ≈ -9.28318

Therefore, log₀,₂8 - log₀,₂200 is approximately equal to -9.28318.