You can put this solution on YOUR website!
Solving equations like this, where the variable is in the argument of one or more logarithms, usually involves transforming the equation into one of the following forms:
log(expression) = other-expression
or
log(expression) = log(other-expression)
With your equation we will use a property of logarithms, , to combine the two logarithms on the left:
This equation now matches the first form above. With this form we proceed by rewriting the equation in exponential form:
Now we have a "regular" equation to solve. We'll start by multiplying both sides by (x+4):
x = 100(x+4)
x = 100x + 400
Subtract 100x from each side:
-99x = 400
Divide both sides by -99:
When solving logarithmic equations you must check your answers. You must ensure that any proposed solutions do not make any arguments to a logarithm zero or negative. (Arguments to logarithms must always be positive!). And when checking, always start with the original equation:
Checking :
As you can see, the argument to the first logarithm is negative. So we must reject this solution. And since this was the only possible solution, there is no solution to your original equation!
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