You can put this solution on YOUR website! log(2x-2) = 4
We start by rewriting the equation in exponential form. In general is equivalent to . Using this pattern on your equation we get: (since the implied base of log is 10)
Simplifying we get:
2x-2 = 10000
Adding 2 we get:
2x = 10002
Dividing by 2 we get:
x = 5001
When solving logarithmic equations we must check our answers. We must ensure that solutions do not make the argument (or base) of any logarithm negative (or zero). This can happen even if no errors were made!
Use the original equation to check:
log(2x-2) = 4
Checking x = 5001:
log(2(5001)-2) = 4
log(10002-2) = 4
We can already see that the argument of the logarithm will be positive. (If it had been negative or zero we would have to reject this solution!) The remainder of the check will just tell us if we made an error. I'll leave that part up to you.
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