Solve for x: log 2 + log(x + 3) - log(3x - 5) = log 3
Share
Solve for x: log 2 + log(x + 3) - log(3x - 5) = log 3
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
To solve the equation log 2 + log(x + 3) - log(3x - 5) = log 3, we can use the properties of logarithms.
Using the property log(a) + log(b) = log(ab), we can rewrite the equation as:
log 2(x + 3) - log(3x - 5) = log 3
Next, using the property log(a) - log(b) = log(a/b), we can simplify further:
log [(2(x + 3))/(3x - 5)] = log 3
Now, we can equate the arguments of the logarithms:
(2(x + 3))/(3x - 5) = 3
To solve for x, we can cross-multiply and solve the resulting equation:
2(x + 3) = 3(3x - 5)
2x + 6 = 9x - 15
Subtracting 2x from both sides:
6 = 7x - 15
Adding 15 to both sides:
21 = 7x
Dividing both sides by 7:
x = 3
Therefore, the value of x that satisfies the equation is x = 3.