Is the answer to 9^2x = 3^x+6 is it -6?
No. Let me see your work.
9^2x= 3^4x
To solve the equation 9^(2x) = 3^(x+6), we can take the logarithm of both sides. The most commonly used logarithm is the natural logarithm, denoted as "ln".
First, we can simplify the equation:
9^(2x) = 3^(x+6)
Taking the logarithm of both sides:
ln(9^(2x)) = ln(3^(x+6))
Using the property log(base b)(a^c) = c * log(base b)(a):
2x * ln(9) = (x+6) * ln(3)
Next, we can simplify further:
2x * ln(9) = x * ln(3) + 6 * ln(3)
Now, we can begin solving for "x". We want to isolate all the terms with "x" on one side of the equation.
Subtracting x * ln(3) from both sides:
2x * ln(9) - x * ln(3) = 6 * ln(3)
Factoring out "x" on the left side:
x * (2 * ln(9) - ln(3)) = 6 * ln(3)
Now, divide both sides by (2 * ln(9) - ln(3)) to solve for "x":
x = (6 * ln(3)) / (2 * ln(9) - ln(3))
Calculating the value, we find:
x ≈ -1.9423408
Therefore, the answer to the equation 9^(2x) = 3^(x+6) is not -6. The value of "x" that satisfies the equation is approximately -1.9423408.