Question

If log10 (a²-15a) = 2, then a= ?

Answer 1

Heya user ,
Here is your answer !!

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log 10 ( a² - 15a ) = 2
=> log 10 ( a² - 15a ) = log 10 100
=> a² - 15a = 100
=> a² - 15a - 100 = 0
=> a² - 20a + 5a - 100 = 0
=> a ( a - 20 ) + 5 ( a - 20 ) = 0
=> ( a + 5 ) ( a - 20 ) = 0 .

So , a can be either -5 or +20 . [ Answer ] .

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Hope it helps !!

Answer 2

log10 (a² - 15a) = 2

we know,
loga X = n
X = aⁿ use this here,

log10 (a² - 15a) = 2
a² - 15a = 10²
a² - 15a - 100 = 0
a² - 20a + 5a - 100 = 0
a(a -20) + 5(a - 20) = 0
(a + 5)(a - 20) = 0
a = 20 , -5
but for log to be defined ,
(a² - 15a)>0 , a> 15 and a<0
so , a = 20 and -5 are solutions of given expression.