How do you solve log (x + 8) = 1 + log (x - 10)?

1 Answer
Dec 14, 2015

x = 12

Explanation:

Begin by moving both of the log terms to the left hand side.

log(x+8) - log(x-10) = 1

Now we can use the division rule for logarithms to combine both terms into one. The division rule states that;

log(m/n) = log(m) - log(n)

Letting m=x+8 and n=x-10, we get;

log((x+8)/(x-10)) = 1

Since we are working with a common log it is base ten. That means that the part inside of the parenthesis is equal to 10 raised to the power of the right hand side, or;

10^1 = (x+8)/(x-10)

Now we just need to do some algebra to solve for x. First, multiply both sides by (x-10).

10(x-10) = x+8

Now multiply the 10 through the parenthesis.

10x - 100 = x + 8

Subtract x and add 100 to both sides.

9x = 108

Finally, divide both sides by 9 to find x.

x = 12