Question

solve the problem

2^log 25 to base 4​

Answer 1

$Given \: \: \: Question \: \: \: \: Is \: \: \\ \\ 2 {}^{ log_{4}(25) } \\ \\ Answer \: \\ \\ \\ 2 {}^{ log_{2 {}^{2} }(25) } \\ \\ 2 {}^{ \frac{1}{2} log_{2}(25) } \\ becoz \: \: \: \: log_{x {}^{n} }(y) = \frac{1}{n} log_{x}(y) \\ \\ 2 {}^{ log_{2}(25) {}^{ \frac{1}{2} } } \\ becoz \: \: \: \: \: \: \frac{1}{n} log_{x}(y) = log_{x}(y) {}^{ \frac{1}{n} } \\ \\ (25) {}^{ \frac{1}{2} } \\ becoz \: \: \: \: \: \: \: \: a {}^{ log_{a}(x) } = x \\ \\ (5 {}^{2}) {}^{ \frac{1}{2} } \\ \\ = 5 \\ \\ \\ Therefore \: \: \: \: \: \: \: \: \: 2 {}^{ log_{4}(25) } = 5$

Answer 2

Answer:

5

Step-by-step explanation:

2^{log 25 to base(2^2)}

= 2^{(1/2)log 25 to base 2} [ lon a to base x^n= (1/n)log a to base x ]

= 2^{log 25^(1/2) to base 2}

=2^{log 5^2^(1/2) to base 2 }

=2^{log 5 to base 2} [ a log x to base a = x ]

= 5