Question

1) log'/2 (2) 2) log3(x^2)÷2log3(x)

Answer 1

Ответ:

1) 2;

2) 1.

Объяснение:

1) log√2 (2) = log√2 (√2) ^2 = 2•log√2 (√2) = 2•1 = 2;

2) log3(x^2)÷(2log3(x) ) = log3(x^2)÷(log3(x^2)) = 1.

Answer 2

1. To simplify the expression log'/2(2), it seems like you're using a notation that is not standard. If you meant to write log base 2 of 2, which can be represented as log₂(2), the answer is 1. This is because the logarithm of a base raised to the power of that base is always equal to 1. In this case, 2 is the base, and 2 raised to the power of 1 is 2.

2. To simplify the expression log₃(x²) ÷ (2 log₃(x)), we can use logarithmic properties to simplify it further.

First, let's rewrite log₃(x²) as 2 log₃(x) using the power rule of logarithms. This gives us:

2 log₃(x) ÷ (2 log₃(x))

Now, we can cancel out the common factor of 2:

log₃(x) ÷ log₃(x)

When we divide two logarithms with the same base, the result is 1. Therefore, the simplified expression is:

1