Question 281036: 2logx=log25; solve for x
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! 2log(x)=log(25)
First use the property of logarithms,  , to move the 2 into the argument as an exponent:
Now, since the logs of  and 25 are equal, they must be equal too:
Since this is a quadratic equation, we want one side to be zero. So subtract 25 from each side:
Then factor:
(x+5)(x-5) = 0
By the Zero Product Property we know that one of these factors must be zero:
x+5 = 0 or x-5 = 0
Solving these we get:
x = -5 or x = 5
When solving logarithmic equations where the variable is in the argument of a logarithm, like this equation, you must check your answers. Even if no errors have been made, you must still check to see if any of your "solutions" make an argument of a logarithm zero or negative. If so we must reject any such "solution" because arguments of logarithms may never be zero or negative.
Always use the original equation to check:
2log(x)=log(25)
Checking x = -5:
2log(-5)=log(25)
As you can see, the logarithm on the left has a negative argument. So we must reject x = -5.
Checking x = 5:
2log(5)=log(25)
As you can see, the logarithm on the left has a positive argument. So this solution will work (if we haven't made any mistakes). (You're welcome to finish the check to see if we made any mistakes.)
P.S. Since you seem to have learned how to use the braces to make your equations look better, you may also want to know how to make your logarithms look better, too.
For base 10 logarithms use: log((argument))
(The extra set of parentheses are intended.)
For base e (aka ln) logarithms use: ln(argument)
For all other bases use: log(base, (argument))
Of course these all go inside the braces.
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