Expert Answers
hala718 eNotes educator| Certified Educator

log 5x - 1 = log 5

Let us move 5 to the left side:

==> log 5x - log 5 - 1 = 0

Now add 1 to both sides:

==> log 5x - log 5 = 1

We know that:

log a - log b = log (a/b)

==> log (5x/5) = 1

==> log x = 1

==> x = 10

 

giorgiana1976 | Student

We know that log 10 = 1 and we'll re-write the equation:

log 5x - log 10 = log 5

We'll use the quotient property, for the difference from the left side:

log 5x/10 = log 5

Because the bases of the logarithms are matching, we'll use one to one property of logarithms:

5x/10 = 5

We'll multiply  by 10 both sides:

5x = 50

We'll divide by 5 both sides:

x = 10

Since x is positive, the equation has the solution x=10.

neela | Student

To solve log5x - 1 = log5

We know logab = loga+logb and log(a/b) = loga-log b.

So the given equation becomes:

log 5+logx  - 1 = log5

logx = log5 - log5 +1

logx = 1

x = 10.

Verication: log5x-1 = log5.

LHS= log5*10 - 1 =

=log50 - log10

= log(50/10)

= log5 = RHS.