6^x^2=600; 10
Correct?
Show your work, please.
I don't have work. it is a Yes or No question in my exam.
Q)Decide if the given number is a solution to the given equation.
Yes or No
The answer should be No.
However, 6 * 10^2 = 600.
To determine if the value of x is correct in the equation 6^x^2 = 600, we need to solve for x.
To solve this exponential equation, we follow these steps:
Step 1: Take the logarithm of both sides of the equation.
Step 2: Apply logarithm properties to simplify the equation.
Step 3: Solve for x using algebraic techniques.
Let's solve it step by step:
Step 1: Take the logarithm of both sides:
log(6^x^2) = log(600)
Using the property log(a^b) = b * log(a), we get:
x^2 * log(6) = log(600)
Step 2: Apply logarithm properties to simplify the equation:
Using the property log(ab) = log(a) + log(b):
x^2 * log(6) = log(6^2) + log(100)
With further simplification:
x^2 * log(6) = 2 * log(6) + log(100)
Step 3: Solve for x using algebraic techniques:
Now we can substitute the value of log(6) which is approximately 0.778 into the equation:
x^2 * 0.778 = 2 * 0.778 + log(100)
Simplifying further:
0.778x^2 = 1.556 + log(100)
Since log(100) equals 2, we can substitute that value:
0.778x^2 = 1.556 + 2
0.778x^2 = 3.556
Finally, solve for x by dividing both sides of the equation by 0.778 and taking the square root:
x = sqrt(3.556 / 0.778)
x ≈ 2.342
Therefore, the solution to the equation 6^x^2 = 600, where x is approximately 2.342, is not equal to 10.