Question

144...is a tough one​

Answer 1

Hey Buddy..

Here's the answer

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$( \sqrt{x} ) ^{ log_{5}(x) - 1 } = 5$

LET

=>

$1 = log_{5}(5)$

=>

$( \sqrt{x} ) ^{ log_{5}(x) - 1} = 5 ^{ log_{5}(5) } \\ \\ ( \sqrt{x} ) ^{ log_{5}(x) - 1 } = {5}^{ log_{5}(5) } \\ \\ (\sqrt{x} ) ^{ log_{5}( {x} ) - 1 } = {5}^{ log_{5}(5) } \\ \\ ( \sqrt{x}) ^{ log_{5}( {x} ) - log_{5}(5) } = {5}^{ log_{5}(5) } \\ \\ ( \sqrt{x}) ^{ log_{5}( {x} \div 5)} = {5}^{ log_{5}(5) }$

Now comparing both sides

=> x / 5 = 5

=> x = 25

For verification

=> √ x = 5

=> x = 25

HOPE HELPED

PEACE

:)

Answer 2

(√x)^( log5 ( x ) - 1 ) = 5

we know

logm ( m ) = 1

so

log5 ( 5 ) = 1

(√x)^( log5 ( x ) - log5 (5) ) = 5^(log5(5)

comparing

x = 25