If log(x) + log(2) = 3, what is the value of x?

If log(x) + log(2) = 3, what is the value of x?

Correct Answer: 1000

Step 1: Start with the equation log(x) + log(2) = 3.
Step 2: Use the property of logarithms that says log(a) + log(b) = log(ab). So, combine the logs: log(2x) = 3.
Step 3: Rewrite the equation in exponential form. This means that if log(2x) = 3, then 2x = 10^3.
Step 4: Calculate 10^3, which is 1000. So now we have 2x = 1000.
Step 5: To find x, divide both sides of the equation by 2: x = 1000 / 2.
Step 6: Calculate 1000 / 2, which equals 500. Therefore, x = 500.

Logarithmic Properties – Understanding how to combine logarithms and apply the properties of logarithms to solve for variables.
Exponential Equations – Converting logarithmic equations into exponential form to isolate the variable.