log 15 (5x+25) = 1

We know that log 15 (15) = 1

==> log 15 (5x + 25) = log 15 (15)

now we know that if log a = log b ==> a= b

==> 5x + 25 = 15

Now divide by 5:

==> x + 5 = 3

==> x= 3-5 = -2

==> x= -2

Let us check answer:

log 15 ( 5x + 25) = log 15 (5*-2 + 25)

= log 15 (-10+25)

= log 15 ( 15)

= 1

We'll impose the constraints of existance of logarithm function.

5x + 25 > 0

We'll add -25 both sides:

5x>-25

We'll divide by 5:

x > -5

So, for the logarithms to exist, the values of x have to belong to the interval (-5, +inf.)

We'll create matching bases to the right side.

Log 15 ( 5x + 25 ) = log 15 (15)

Now, because the bases are matching, we'll apply the one to one property:

5x + 25 = 15

We'll subtract 25 both sides:

5x = 15-25

5x = -10

We'll divide by 5:

**x = -2 > -5**

Since the value for x belongs to the interval (-5,+inf.), the solution is valid.

log15 (5x + 25) =1

To find x.

Solution:

Left side is logarithm to base 15. Therefore we convert right side term 1 into the log arithm to vase 15 as: 1 = log15 (15). So now the given equation becomes:

log15 (5x+25) = log15 (15). Now we take the antilogarithms.

5x+25 = 15.

Subtract 25.

5x = 15-25 = -10

x = -10/5 = -2.