Solving an equation where the variable is in the argument of a logarithm usually starts with transforming the equation into one of the following forms:
log(variable-expression) = other-expression
or
log(variable-expression) = log(other-expression)
With the term of 1 on the right side, it will be difficult to get an "all logarithm" equation like the second form. So we will aim for the first form. This will require that we combine the two logarithms into one. Fortunately there is a property of logarithms we can use: . Using this on your equation we get:
We now have the equation in the desired form. With this form proceed by rewriting the equation in exponential form. This equation in exponential form is:
which simplifies to:
We now have an equation without logarithms to solve. We'll multiply both sides by (x+1) to get rid of the fraction:
which simplifies to:
Subtract 10 from each side:
Divide both sides by 10:
We should check this answer not because it is generally a good idea but because we multiplied both sides by (x+1). (x+1) might be zero depending on the value of x. Whenever you multiply both sides of an equation by an expression that might be zero, you need to check your answer. If your answer makes this expression zero, then your answer does not actually fit the original equation. So in this situation you must check your answer.
Checking x = 1.5:
Using the property to combine the logarithms: Check!
(