Question

log (log(a2-a-20))=0 for a>0,then a ?​

Answer 1

Step-by-step explanation:

Solve for log thn quadratic

Answer 2

SOLUTION

GIVEN

$\sf \log( \log \: ( {a}^{2} - a - 20 )) = 0 \: \: \: with \: a > 0$

TO DETERMINE

$\sf \log( \log \: ( {a}^{2} - a - 20 )) = 0$

$\sf \implies \: \log( \log \: ( {a}^{2} - a - 20 )) = \log 1$

$\sf \implies \: \log \: ( {a}^{2} - a - 20 )= 1$

$\sf \implies \: \log \: ( {a}^{2} - a - 20 )= \log 10$

$\sf \implies \: \: ( {a}^{2} - a - 20 )= 10$

$\sf \implies \: \:{a}^{2} - a -30= 0$

$\sf \implies \: \:{a}^{2} - (6 - 5)a -30= 0$

$\sf \implies \: \:{a}^{2} - 6a + 5a -30= 0$

$\sf \implies\:(a - 6)(a + 5)= 0$

$\sf \implies \: a = - 5 \: , \: 6$

Since a > 0

∴ a ≠ - 5

∴ a = 6

FINAL ANSWER

Hence the required value of a = 6

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