SOLUTION: If (log_9)4=a and (log_27)5=b, find and expression in terms of a and b for log_(square root over 3)40

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Question 177206: If (log_9)4=a and (log_27)5=b, find and expression in terms of a and b for log_(square root over 3)40
Answer by stanbon(57967) About Me  (Show Source):
You can put this solution on YOUR website!
If (log_9)4=a
So 9^a = 4
Therefore (sqrt(3))^(4a) = 4
And log(sqrt(3)4 = 4a
Also log(sqrt(3)2 = 2a
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and (log_27)5=b
So 27^b = 5
Therefore (sqrt(3))^(6b) = 5
And log(sqrt(3)5 = 6b
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find and expression in terms of a and b for log_(square root over 3)40
log(sqrt(3))40 = log(sqrt(3)[2*4*5]
log(sqrt(3))2 + log(sqrt(3)4 + log(sqrt(3)5
= 2a + 4a + 6b
= 6(a+b)
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Cheers,
Stan H.