Final answer:
To solve the equation log(x) + 9 - log(2) = log(4x) + 3, we combine and simplify the log terms, equate the arguments, and solve for x which involves calculating 10^(6) to find the value of x.
Step-by-step explanation:
To solve the logarithmic equation log(x) + 9 - log(2) = log(4x) + 3, we can use properties of logarithms to combine terms and then solve for x. First, we rewrite the equation by factoring out the logs where possible and then simplify the equation using logarithmic properties. Here's the step-by-step process:
- Combine the log terms on each side: log(x) - log(2) = log(4x) - 6.
- Apply the property log(a) - log(b) = log(a/b) to the left side: log(x/2) = log(4x) - 6.
- Next, we can equate the arguments of the logarithms since if log(a) = log(b), then a = b: x/2 = 4x * 10^(-6).
- Solve the resulting equation for x.
To find x, we multiply both sides by 2 and then divide by 4x: x = 4x * 2 * 10^(-6).
Now, solving the equation we have: x = 8x * 10^(-6). To find the value of x, divide both sides by 8 * 10^(-6), which gives us x = 1/(10^(-6)).
Finally, to obtain the value of x, we use the inverse log or calculate 10^(6) to find x.