Question

if 2 log 5 +log 8-1/2 log 4 =k find k-2​

Answer 1

Answer:

I think answer is 0.

Step-by-step explanation:

2log5 + log8 - 1/2log4 = k

2log5 + 3log2 - log2 = k

2( log5 + log2) = k

2(log 2×5) = k

2log10 = k

therefore 10² = 10^k

so, k=2 and k-2 = 0 = ans

Answer 2

GIVEN :–

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$\sf \implies 2 log(5) + log(8) - \dfrac{1}{2} log(4) = k$

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TO FIND :–

• k - 2 = ?

SOLUTION :–

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$\sf \implies 2 log(5) + log(8) - \dfrac{1}{2} log(4) = k$

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• Using identity –

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$\bf \: \implies alog(b) = log( {b}^{a} )$

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$\sf \implies 2 log(5) + log(8) - log(4^{\frac{1}{2})} = k$

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$\sf \implies 2 log(5) + log( {2}^{3} ) - log(2) = k$

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$\sf \implies 2 log(5)+3log(2) - log(2) = k$

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• We know that –

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$\bf \: {\huge{.}} \: \: \: log(5) =0.7$

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$\bf \: {\huge{.}} \: \: \: log(2) =0.3010$

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• So that –

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$\sf \implies 2(0.7)+3(0.3010) - 0.3010 = k$

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$\sf \implies 2(0.7)+2(0.3010) = k$

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• By Approximation –

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$\sf \implies 2(0.7)+2(0.3) = k$

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$\sf \implies 2(0.7 + 0.3)= k$

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$\sf \implies k = 2(1)$

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$\sf \implies k = 2$

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• Hence –

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$\sf \implies k - 2 = 2 - 2$

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$\sf \implies \large{ \boxed{ \sf k - 2 =0}}$