If \(\log_{10}\)(6x - 4) - \(\log_{10}\)2 = 1, solve for x.
Question 1 Report
If \(\log_{10}\)(6x - 4) - \(\log_{10}\)2 = 1, solve for x.
Answer Details
To solve for x, we can use the following steps:
1. Rewrite the equation using exponential form: 10^(log(6x - 4) - log(2)) = 10^1
2. Use the fact that log(a) - log(b) = log(a/b) to simplify the equation: 10^(log((6x - 4) / 2)) = 10^1
3. Use the definition of logarithms to simplify the equation: (6x - 4) / 2 = 10
4. Solve for x by multiplying both sides of the equation by 2 and then subtracting 4 from both sides: 6x - 4 = 20, 6x = 24, and x = 4
So, the solution to the equation is x = 4.
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