We have log (7) a + log (a) 7 =
2
We use the relation for logarithms that log a + log b =
log (a*b) and log (a) b = 1 / log(b) a.
log (7) a + log (a)
7 = 2
=> log (7) a + 1/ log (7) a =
2
=> [log (7) a]^2 + 1 = 2* log(7)
a
=> [log (7) a]^2 + - 2* log(7) a + 1 =
0
=> (log(7) a - 1)^2 =
0
=> log(7) a =
1
=> a =
7
The required solution is a =
7.
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