- #1
juliany
- 11
- 0
Homework Statement
Solve: log3^(2x-9)-2log3^x=-2
Homework Equations
None
The Attempt at a Solution
I am confused with one part of this equation.
With the 2log3^x, can you move the x to the front to make it 2x log3?
To solve this equation, first isolate the logarithms on one side of the equation by adding 2xlog3 to both sides. This will result in log3^(2x-9) = 2xlog3 - 2x. Then, use the properties of logarithms to rewrite the equation as log3^(2x-9) = log3^(2x) - log3^(2). Since the bases of the logarithms are the same, we can set the exponents equal to each other, resulting in 2x-9 = 2x - 2. From here, it is a simple algebraic equation to solve for x.
Yes, you can use any base for this equation. However, it may be easier to solve if you use the same base on both sides of the equation.
The domain of this equation is all real numbers, except for x = 3/2. This is because when x = 3/2, the logarithms will result in an undefined value.
Yes, it is possible to solve this equation without using logarithms. However, the resulting equation will be more complex and may be more difficult to solve algebraically.
To check your answer, you can plug it back into the original equation and see if it satisfies the equation. Another way to check is to graph both sides of the equation on a graphing calculator and see if they intersect at the same point, which would indicate that the value of x is correct.