log 5x - log 7 = log 32 + 5log
5
Let us rewrite 32 =
2^5
==> log 5x - log 7 = log 2^5 + 5log
5
==> log 5x - log 7 = 5log 2 + 5log
5
We have 5 is a common
factor:
==> log 5x - log 7 = 5(log 2 + log
5)
Now we know that:
log a +
log b = log a*b
log a - log b = log
(a/b)
==> log (5x/7) = 5log
(2*5)
==> log (5x/7) = 5 log
10
But, log 10 = 1
==>
log (5x/7) = 5
==> 5x/7 =
10^5
==> 5x =
7*10^5
==> x= (7*10^5)/5= 14*10^4=
140000
==> x= 140,000
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