solve the equation
2logx+log4=2
Can someone walk me through this
use the rules of logs
2logx + log4 = 2
log(x^2) + log4 = 2
log (4x^2) = 2
4x^2 = 10^2
4x^2 = 100
x^2 = 25
x = ± 5, but we cannot take log(-5)
so x = 5
test my answer with your calculator
Sure, I can help you with that!
To solve the equation 2logx + log4 = 2, we need to isolate the logarithmic term and then solve for x. Here's how you can do it step by step:
Step 1: Combine the logarithms using the log properties. In this equation, we can use the property log a + log b = log (a * b). Applying this property, the equation becomes:
log (x^2) + log 4 = 2.
Step 2: Simplify the equation further. Remember that log a + log b = log (a * b). Using this property again, the equation can be rewritten as:
log (x^2 * 4) = 2.
Step 3: Remove the logarithm by exponentiating both sides of the equation. The exponentiation property states that if log a (x) = y, then a^y = x. Applying this property, we have:
10^2 = x^2 * 4.
Step 4: Simplify the equation:
100 = 4x^2.
Step 5: Divide both sides of the equation by 4 to solve for x^2:
25 = x^2.
Step 6: Take the square root of both sides of the equation:
x = ±5.
So, the solutions to the equation 2logx + log4 = 2 are x = 5 and x = -5.