Question

Log4 log5 25 =????? Если сможете,то обьясните как вы решили это

Answer 1

Log₄log₅25=log₄log₅5²=(1/2)log₂(2log₅5)=(1/2)log₂2=1/2

Answer 2

Logarithmic Calculation

To solve the equation log4(log5(25)), we need to understand the properties of logarithms and how to apply them.

The equation consists of nested logarithmic functions. Let's break it down step by step:

1. Start with the innermost logarithm, which is log5(25). This means we need to find the logarithm of 25 with a base of 5.

According to the logarithmic property, logb(x) = y is equivalent to b^y = x. In this case, we have log5(25) = y, which means 5^y = 25.

To find the value of y, we can rewrite 25 as a power of 5: 25 = 5^2. Therefore, 5^y = 5^2.

By equating the exponents, we get y = 2.

So, log5(25) = 2.

2. Now that we have the value of the inner logarithm, we can substitute it into the outer logarithm.

The equation becomes log4(2), which means we need to find the logarithm of 2 with a base of 4.

Using the same logarithmic property, we have log4(2) = y, which means 4^y = 2.

To solve for y, we can rewrite 2 as a power of 4: 2 = 4^(1/2). Therefore, 4^y = 4^(1/2).

By equating the exponents, we get y = 1/2.

So, log4(2) = 1/2.

3. Therefore, the solution to the equation log4(log5(25)) is 1/2.

Explanation:

To solve the equation log4(log5(25)), we need to understand the properties of logarithms and how to apply them.

1. First, we evaluate the innermost logarithm, which is log5(25). This means we need to find the logarithm of 25 with a base of 5. - Using the logarithmic property logb(x) = y is equivalent to b^y = x, we can rewrite the equation as 5^y = 25. - To find the value of y, we can rewrite 25 as a power of 5: 25 = 5^2. - By equating the exponents, we get y = 2. - Therefore, log5(25) = 2.

2. Now that we have the value of the inner logarithm, we can substitute it into the outer logarithm. - The equation becomes log4(2), which means we need to find the logarithm of 2 with a base of 4. - Using the logarithmic property logb(x) = y is equivalent to b^y = x, we can rewrite the equation as 4^y = 2. - To solve for y, we can rewrite 2 as a power of 4: 2 = 4^(1/2). - By equating the exponents, we get y = 1/2. - Therefore, log4(2) = 1/2.

3. Therefore, the solution to the equation log4(log5(25)) is 1/2.

Please note that the above explanation is based on the properties of logarithms and the given equation. The solution may vary depending on the context or specific requirements of the problem.