2 log x- log 9=log 441
2Logx - Log9 = Log441.
Logx^2 = Log441 + Log9
Logx^2 = Log(441*9)
Logx^2 = Log3969
x^2 = 3969
X = 63
To solve the equation 2log(x) - log(9) = log(441), we can use the logarithmic properties.
1. Begin by using the power rule of logarithms, which states that log(a) - log(b) = log(a/b). Applying this rule to the equation, we have:
2log(x) - log(9) = log(441)
log(x^2) - log(9) = log(441)
2. Next, combine the logarithms on the left side of the equation using the product rule, which states that log(a) + log(b) = log(ab):
log(x^2 / 9) = log(441)
3. Use the fact that log(a) = log(b) if and only if a = b. Therefore, we can equate the arguments inside the logarithms:
x^2 / 9 = 441
4. To isolate x, multiply both sides of the equation by 9:
x^2 = 441 * 9
Simplifying:
x^2 = 3969
5. Take the square root of both sides:
x = ±√3969
6. Finally, evaluate the square root:
x = ±63
Therefore, the two possible solutions for x are x = 63 and x = -63.
To solve the equation 2log(x) - log(9) = log(441), we will use logarithmic properties and algebraic manipulations.
First, we need to express all the logarithms on one side of the equation. We can do this by combining the two logarithms on the left-hand side using the property log(a) - log(b) = log(a/b):
2log(x) - log(9) = log(441)
log(x^2) - log(9) = log(441)
Next, we can use the property log(a) - log(b) = log(a/b) again to simplify the equation further:
log(x^2) - log(9) = log(441)
log(x^2/9) = log(441)
Now, to remove the logarithm and solve for x, we can equate the arguments of the logarithms:
x^2/9 = 441
To isolate x^2, we can multiply both sides of the equation by 9:
x^2 = 441 * 9
Simplifying further:
x^2 = 3969
To find the value of x, we can take the square root of both sides of the equation:
x = ±√3969
The square root of 3969 is 63, therefore:
x = ±63
So the solutions to the equation 2log(x) - log(9) = log(441) are x = -63 and x = 63.