Question

(√2 )^(log2 5) ∙ log 3(27)

Answer 1

Примерно 21 ((((((((((()))))))))))

Answer 2

To simplify the expression (√2)^(log2 5) * log3(27), let's break it down step by step.

Step 1: Simplify the exponent (√2)^(log2 5). To simplify this, we need to apply the properties of exponents. When a base is raised to a power and then raised to another power, we multiply the exponents. In this case, (√2)^(log2 5) can be rewritten as 2^(1/2)^(log2 5). Applying the exponent property, we have 2^[(1/2) * (log2 5)]. Now, we can simplify the exponent by multiplying the fractions: (1/2) * (log2 5) = log2 5^(1/2). Therefore, (√2)^(log2 5) simplifies to 2^(log2 5^(1/2)).

Step 2: Simplify log3(27). The logarithm with a base of 3 of 27 can be expressed as log3 27 = 3. This is because 3^3 = 27.

Now, we can combine the simplified expressions: 2^(log2 5^(1/2)) * log3(27) = 2^(log2 5^(1/2)) * 3 = 2^(log2 √5) * 3

The expression 2^(log2 √5) represents raising 2 to the power of the logarithm base 2 of the square root of 5. Since the base of the logarithm is 2, and we are raising 2 to that power, we end up with √5. Therefore, we can simplify the expression further:

= √5 * 3 = 3√5

So, the simplified form of the expression (√2)^(log2 5) * log3(27) is 3√5.