Question

value of 361 raised to power log 5 to the base 19
​

Answer 1

SOLUTION

TO DETERMINE

The value of

$\displaystyle \sf{ {361}^{ log_{19}(5) } }$

EVALUATION

Let

$\displaystyle \sf{ {361}^{ log_{19}(5) } = x }$

Taking logarithm in both sides we get

$\displaystyle \sf{ log_{19}(5) = log_{361}(x) }$

$\displaystyle \sf{ \implies log_{361}(x) = log_{19}(5) }$

$\displaystyle \sf{ \implies \frac{ log(x) }{ log(361) } = \frac{ log(5) }{ log(19) } }$

$\displaystyle \sf{ \implies \frac{ log(x) }{ log( {19}^{2} ) } = \frac{ log(5) }{ log(19) } }$

$\displaystyle \sf{ \implies \frac{ log(x) }{2 log( {19}) } = \frac{ log(5) }{ log(19) } }$

$\displaystyle \sf{ \implies \frac{ log(x) }{2 } = log(5) }$

$\displaystyle \sf{ \implies log(x) = 2 log(5) }$

$\displaystyle \sf{ \implies log(x) = log( {5}^{2} ) }$

$\displaystyle \sf{ \implies log(x) = log(25) }$

$\displaystyle \sf{ \implies x = 25 }$

FINAL ANSWER

Hence the required value of x = 25

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