log 5x - log 7 = log 32 + 5log5

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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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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