You can put this solution on YOUR website!
To combine these logarithms we'll use one of the properties of logarithms:
Using this property on the left side of your equation we get:
Now that the equation is in the form of
log(expression) = other-expression
we can solve it by rewriting the equation in exponential form. In general is equivalent to . Using this pattern on your equation we get:
Since this is:
This equation we can solve. Since it is a proportion (A "fraction equals a fraction" equation is called a proportion.) we can cross-multiply:
(8x-13)3 = (12x+21)1
Simplifying each side we get:
24x-39 = 12x + 21
Subtracting 12x from each side:
12x + 39 = 21
Subtracting 39 from each side:
12x = -18
Dividing both sides by 12:
which reduces to
When solving logarithmic equations you must check your answer(s). You must ensire that your answer(s) make all arguments to logarithms positive. Any "solution" that make an argument zero or negative must be rejected.
Use the original equation to check:
Checking x = -3/2:
Simplifying:
As we can see, the first argument if negative. So we must reject this "solution". (Arguments to logarithms must be positive.) And since this was the only solution we found, there is no solution to your equation.
(