2 log power
15 to the base 2 root 2
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We know that a^(log x to the base a) = x and log a to the base b= 1/log b to the base a. Also log a^m to the base b=m.log a to the base b.
So 2^{log 15 to the base 2√2}
=2^{1/log 2√2 to the base 15}
=2^{1/log 2^(3/2)to the base 15}
=2^{1/(3/2)log 2 to the base 15}
=2^{2/3) log 15 to the base 2
=2^{log 15^(2/3) to the base 2
=15^(2/3).
So 2^{log 15 to the base 2√2}
=2^{1/log 2√2 to the base 15}
=2^{1/log 2^(3/2)to the base 15}
=2^{1/(3/2)log 2 to the base 15}
=2^{2/3) log 15 to the base 2
=2^{log 15^(2/3) to the base 2
=15^(2/3).
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