Maths easy problem....... REPLY ASAP?

Question

SHOW ALL STEPS WHEN SOLVING:
log x + log (x-9) = 1

Answer 1

logx+log(x-9)=1
logx(x-9)=1 product rule
x(x-9)=10 definition of log
x^2-9x-10=0
(x_10)(x+1)=0
x-10=0 or x=10
x+1=0 or x=-1
ignoring the negative value x=10

Answer 2

We can raise any number to the power of both sides. Since we're working with common logs, we'll use 10.

10^[log x + log(x-9)] = 10^1

Now, a number raised to the power of a sum is equal to the product of the number raised to the power of the first addend and the number raised to the power of the second addend. That is:

a^(b+c) = (a^b)*(a^c)

So:

(10^log x) [10^log(x-9)] = 10


At this point, we observe that

10^(log x) = x.

The number doesn't have to be 10. If you raise a to the power of log base of x, the result is x.

This means that

(10^log x) [10^log(x-9)] = x(x - 9)

x(x-9) = 10
x^2 - 9x - 10 = 0
(x - 10)(x + 1) = 0

x = 10 or x = -1

We can't take the log of a negative number in the set of real numbers. So x = 10 is the only solution.

Check:

log(10) + log(10 - 9) = 1
1 + log(1) = 1
1 + 0 = 1

It works!

Answer 3

log x + log(x-9) = 1

Use the log addition rule; the sum of two logs is the product of their inside functions.

log(x*(x-9)) = 1

Change to exponential form. When doing this, remember that the base of the log becomes the base of the exponent, and the inside of the log becomes the answer. Assuming this is base 10:

10^(1) = x(x-9)

Solve as normal.
10 = x^2 - 9x
x^2 - 9x - 10 = 0

This is a quadratic, so factor.
(x-10)(x+1) = 0
x = 10 or x = -1

From this point, you have to test both solutions to determine if they both work, in the original equation. Reminder: You CANNOT take the log of a negative number.

Test x = 10: log10 is valid, and log (10-9) = log(1) is valid.
Test x = -1: log(-1) is invalid, so you throw away x=-1 solution.

Therefore, the answer is x = 10

Answer 4

Ok, let's try this one,

recall that log(AB) = log(A) + log(B)

so,

log(x(x-9)) = 1

raise both sides to the tenth power...you will get

x(x-9) = 10

x^2 - 9x - 10=0

solving the quadratic equation you will get

(x-10)(x+1) = 0

Pick the positive root (the log of a negative number is not defined for real numbers)

x =10

Good luck.

Answer 5

raise both sides to the 10th power
10^(log x+log(x-9))=10^1

a^(b+c)=a^b*a^c
10^(log x)*10^log(x-9)=10^1

since log is base 10
x(x-9)=10

distribute
x^2-9x-10=0

factor
(x-10)(x+1)=0

answer
x=10 or -1

Answer 6

do your own homework!