- #1
tommy2st
- 15
- 0
Homework Statement
log6(x+6) - log6(x-4) = 3
2. The attempt at a solution
150/36 is what i get which i simplified to 25/6.
but the program tells me I am wrong can anyone think of how I am getting this wrong
lewando said:I get something close, what steps did you do to get at that answer?
To solve a log equation, you can use the properties of logarithms and algebraic manipulation. In this case, we can combine the two logs using the quotient property and then solve for x.
The quotient property states that logb(x/y) = logb(x) - logb(y). In this equation, we have log6(x+6) - log6(x-4) = 3, so we can rewrite it as log6((x+6)/(x-4)) = 3.
To graph logarithmic functions, you can first determine the domain and range of the function and then plot points to create a smooth curve. In this equation, the domain is restricted to (4, infinity) since log6(x-4) must be positive, and the range is all real numbers. You can also use a graphing calculator to graph logarithmic functions.
In logarithmic equations, it's possible to get extraneous solutions, which are values that satisfy the equation but are not valid solutions. To check if a solution is extraneous, you can plug it back into the original equation and see if it results in a negative or undefined value under the logarithm.
Yes, you can use a calculator to solve this equation. You can use the log function on your calculator to find the logarithm of each side of the equation, and then use algebra to isolate x. Just be careful to check for extraneous solutions when using a calculator.