If log7 (a) + loga (7) = 2, what is a?
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calendarEducator since 2008
write3,662 answers
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log7 (a) + loga ( 7) = 2
We will rewrite using the logarithm properties.
We know that:
log7 (a) = loga (a) / loga (7)
But loga a = 1
==> log7 (a) = 1/loga (7)
Let us substitute into the equation.
==> 1/loga (7) +loga (7) = 2
==> Multiply by loga (7)
==> 1 + ( loga (7))^2 = 2loga (7)
Let us assume that loga (7) = x
==> 1 + x^2 = 2x
==> x^2- 2x +1 = 0
==> (x-1)^2 = 0
==> x = 1
==> loga (7) = 1
==> a = 7
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calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
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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