If $l o g_{2} x = a$ and $l o g_{5} y = a$ , write $10 0^{2 a - 1}$ in terms of x and y.

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l o g_{2} x = a

and

l o g_{5} y = a

, write

10 0^{2 a - 1}

in terms of x and y.

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Text solutionVerified

$l o g - 2 x = a ∴ x = 2^{a} an d l o g g_{5} y = a t h e n y = 5^{a} t h e n x y = 2^{a} 5^{a} x y = 1 0^{a} ∴ 10 0^{2 a - 1} = (\frac{10 0 ^{2 a}}{100}) = (\frac{1 0 ^{4 a}}{100}) = (\frac{( 1 0 ^{a} ) ^{4}}{100}) = (\frac{( x y ) ^{4}}{100})$

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Question Text	If $l o g_{2} x = a$ and $l o g_{5} y = a$ , write $10 0^{2 a - 1}$ in terms of x and y.
Answer Type	Text solution:1
Upvotes	152

If log2​x=a and log5​y=a, write 1002a−1 in terms of x and y.

Text solutionVerified

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If $l o g_{2} x = a$ and $l o g_{5} y = a$ , write $10 0^{2 a - 1}$ in terms of x and y.