logx + log (x-15)=2?

Question

I have to describe in complete sentences the steps to be taken in order to solve the log equation.

Answer 1

Take log as log to base ten.
x (x - 15) = 10²
x² - 15x - 100 = 0
(x - 20)(x + 5) = 0
x = 20 , x = - 5
Accept 20 as answer (- 5 is not acceptable)

Answer 2

Use the log property that says log(ab) = log a + log b

log[(x(x-15)] = 2

Take 10^(each side)

x(x-15) = 10^2 = 100

Solve for x

x^2 - 15x = 100

x^2 - 15x - 100 = 0

Factor the above polynomial

(x-20)(x+5) = 0

This would give you x=20 or x=-5

But if you try to put the above back into the equation, you'll find out that you cannot take the log of a negative number.

So your only answer is x=20

Answer 3

Remember that adding 2 logs is the same as multiplying the parts being logged:

log(x*(x-15) = 2
log (x^2 -15x) = 2

Now take the anti-logs (the anti-log of 2 is 100, i.e. the number whose log is 2 is 100):

x^2-15x = 100

x^2 - 15x - 100 = 0

Just from casual inspection:

(x-20)(x + 5) = 0

So x = 20 or -5.

Forget -5, because you can't have the log of a negative number.

Now let's check out the answer in the original statement:

Log 20 + log 5 = 2

Log 20 =1.301

Log 5 = .699

Total = 2

Answer 4

One property of logarithms is that you can multiply the x and x-15 if you multiply them together. Also remember, log is base 10 by default.

Lets add the logs by multiplying the ingredients. We now have log x^2-15x=2

Here's where the base 10 comes into play.

10^2 = x^2-15x (this is what a logarithm says: Base to the answer power equals the x^2-15x)

Now we can solve that by subtracting 100 from both sides and then factoring.

x^2-15x-100=0

Factor

(x-20)(x+5)

x equals 20 or -5

Logs can't be negative, so 20 is your only answer.

Answer 5

You have a sum of logs.
log a + log b = log(a*b)
After you do that you will have
log(something) = 2
Now you have 2 things that are = and one of the 2 involves logs of a variable. You can "get rid" of the log(something) by makeing the 2 things that are = the exponents on 10.
Then you would have
something = 10^2
Looking ahead you would then be solving a quadratic equation either by factoring or using the quadratic formula.

Answer 6

log (x^2 - 15x) = 2
x^2 - 15x = 100
x^2 - 15x - 100 = 0
(x-20)(x+5) = 0
x = 20 or -5
-5 is invalid answer
x = 20