Question

6^2log6 5 (6 основание)

Answer 1

Ответ:

25

Объяснение:

1) Преобразовать выражение:

${6}^{ log_{6}( {5}^{2} ) }$

2) Упростить выражение:

${5}^{2}$

3) Вычислить степень:

$25$

Answer 2

To evaluate the expression 6^2 * log6(5), we first need to understand the meaning of the notation.

1. 6^2 means 6 raised to the power of 2, which is 6 * 6 = 36.
2. log6(5) means the logarithm of 5 with base 6.

Now, we need to calculate the logarithm. The logarithm function tells us what exponent we need to raise the base (in this case, 6) to get the given number (in this case, 5).

So, log6(5) is the exponent we need to raise 6 to in order to get 5. Therefore, log6(5) = x can be rewritten as 6^x = 5.

Now, to solve for x, we can take the logarithm base 6 of both sides:

log6(6^x) = log6(5)

Using the property of logarithms that log_b(b^x) = x:

x = log6(5)

Now, we need to calculate log6(5). This can be done using a calculator, as follows:

x ≈ 1.4649735

Now, we can substitute this value back into the original expression:

6^2 * log6(5) ≈ 36 * 1.4649735 ≈ 52.736946