Question

Найдите значение выражения. 2 в степени логарифм 27 по основанию 8

Answer 1

2 в степени log 27 по основанию 8 равно 2 в степени 27 по снованию 2 в степени 3 равно 2 в степени 3*log 27 по основанию 2 равно 3*27 равно 81. Я думаю что так.

Answer 2

Calculating the Value of \(2\) to the Power of the Logarithm of \(27\) with Base \(8\)

To find the value of \(2\) to the power of the logarithm of \(27\) with base \(8\), we can use the property of logarithms: \(a^{\log_a{b}} = b\), where \(a > 0\), \(a \neq 1\), and \(b > 0\). This property states that if we have \(a\) raised to the power of the logarithm of \(b\) with base \(a\), the result is \(b\).

Solution

Using the property mentioned above, we can express the given expression as: \[2^{\log_8{27}}\]

Now, according to the property, \(2^{\log_8{27}} = 27\). Therefore, the value of \(2\) to the power of the logarithm of \(27\) with base \(8\) is 27.

This conclusion is supported by the mathematical property of logarithms and exponentiation, as described above.

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