2 log x- log 9=log 441
log x^2 - log9 = log 441
log (x^2 /9) = log 441
"antilog" it
x^2/9 = 441
x^2 = 3969
x = ±63 , but we cannot take log of a negative, so
x = 63
To solve the equation 2 log x - log 9 = log 441, we can use logarithmic properties and algebraic manipulations to simplify the equation and find the value of x.
Step 1: Apply logarithmic properties
We can use the properties of logarithms to rewrite the equation as a single logarithm:
log x^2 - log 9 = log 441
Step 2: Apply the division property of logarithms
Using the division property of logarithms (log a - log b = log (a/b)), we can simplify the equation further:
log (x^2/9) = log 441
Step 3: Remove the logarithm
Since the logarithm is the same on both sides of the equation, we can remove it:
x^2/9 = 441
Step 4: Solve for x
To solve for x, we can multiply both sides of the equation by 9:
x^2 = 9 * 441
x^2 = 3969
Taking the square root of both sides:
x = ± √3969
x = ± 63
So, the solution to the equation is x = ± 63.