Question

mathFind a if 729^a - 57=0.

Accepted Answer

We need to find a if 729^a - 57 = 0
729^a - 57 = 0
=> 729^a = 57
As the base cannot be equated we can use logarithms
log (729^a) = log 57
use the property log a^b = b*log a
=> a*log 729 = log 57
=> a = log 57 / log 729
The value of a = log 57/log 729

Answer

We notice that we don't have common bases. We'll use logarithms to determine  the variable a.
We'll take logarithms both sides:
log3 (9^3a) = log3 57
We'll use power property of logarithms:
3a*log3 9 = log3 57
But log3 9 = log3 3^2, where log3 3 = 1
log3 3^2 = 2log3 3
log3 3^2 = 2
3a*2 = log3 57
6a = log3 3*19
We'll use product property of logarithms:
6a = log3 3 + log3 19
6a = 1 + log3 19
log3 19 = lg 19/lg 3
log3 19 = 2.70
We'll divide by 6:
a = 1/6 + 2.70/6
a = 0.16 + 0.45
a = 0.61

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math Find a if 729^a - 57=0.

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