Question

Вычислите значение выражения log4 50-log4 25

Answer 1

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Answer 2

$\displaystyle log_{4}50-log_{4}25=log_{4}\left(\frac{50}{25}\right)=log_{4}2=\frac{1}{2}=0,5$

Answer 3

To compute the value of the expression log₄50 - log₄25, we can use the properties of logarithms. One of the properties states that logₐ(b) - logₐ(c) is equal to logₐ(b/c).

So, in our case, we have:

log₄50 - log₄25 = log₄(50/25)

Now, simplify the expression inside the logarithm:

log₄(50/25) = log₄(2)

The value of log₄(2) represents the power to which 4 must be raised to get 2. So, we can say:

4^x = 2

To find x, we can rewrite the equation in exponential form:

x = log₂(4)

Now, use the base conversion formula: logᵦ(a) = logₓ(a) / logₓ(ᵦ).

In this case, b = 2 and a = 4:

x = log₂(4) = log₄(4) / log₄(2)

Since log₄(4) is equal to 1 (as 4^1 = 4), we have:

x = 1 / log₄(2)

Now, we need to calculate log₄(2):

log₄(2) ≈ 0.5 (approximately)

Now, substitute the value of log₄(2) back into the equation:

x ≈ 1 / 0.5 ≈ 2

So, log₄50 - log₄25 is approximately equal to 2.