Question

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Maths ch1 SM pg1.37 Q.20
If (5.678)^x=(0.5678)^y=10^z then
Plz. explain in detail step by step
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Answer 1

Hey Mate here is your answer ✌️☺️

Answer 2

Answer:

Required correct option is option ( b ).

Step-by-step-explanation:

Given : ( 5.678 )^x = ( 0.5678 )^y = 10^z .

Let the given terms are also equal to k.

Thus,

= > ( 5.678 )^x = ( 0.5678 )^y = 10^z = k

Then,

Case 1 : where ( 5.678 )^x = k

= > ( 5.678 )^x = k

= > 5.678 = k^( 1 / x ) ...( 1 )

Case 2 : where ( 5.678 )^x = k

= > ( 0.5678 )^y = k

= > 0.5678 = k^( 1 / y ) ...( 2 )

Case 3 : where 10^z = k

= > 10^z = k

= > 10 = k^( 1 / z ) ...( 3 )

Multiplying ( 1 ) & ( 3 ) and dividing by ( 2 ) : -

= > ( 5.678 × 10 / 0.5678 ) = [ k^( 1 / x ) × k^( 1 / z ) ] / [ k^( 1 / y ) ]

= > 100 = k^{ 1 / x + 1 / z - 1 / y ]

= > 10^2 = k^( 1 / x + 1 / z - 1 / y ]

= > { k^( 1 / z )}^2 = k^( 1 / x + 1 / z - 1 / y ) { from ( 3 ), 10 = k^( 1 / z ) }

= > k^( 2 / z ) = k^( 1 / x + 1 / z - 1 / y )

= > 2 / z = 1 / x + 1 / z - 1 / y

= > 0 = 1 / x + 1 / z - 2 / z - 1 / y

= > 0 = 1 / x - 1 / z - 1 / y

Hence the required correct option is ( b ).