Originally Posted by

**B9766** I'm having trouble with a statement in the text that says, "the equation $log_{10}\ (x +\ 10)\ \neq \ log_{10}\ x\ +\ log_{10}\ 10$ for all values of x. However, you can show that this equation does have a solution: $x\ =\ 10/9$

I understand the first part of the statement but haven't been able to figure out how they arrived at $x\ =\ 10/9$.

I tried starting with $f(x)\ = \ log\ (x\ +\ 10)$ and then solving for x. But doing so I get:

$y\ = \ log(x\ +\ 10)$

$y^{10}\ =\ (x\ +\ 10)$

$x\ =\ y^{10}\ -\ 10$ and that's clearly not $10/9$

I also tried substituting $10/9$ in the first statement:

$log(10/9\ +\ 10)\ =\ log(\frac{10+90}{9})\ =\ log(100/9)\ =\ log(10^2)\ -\ log(9)\ = 2(1)\ -\ log(9)$ and that's not $10/9$

I would appreciate help solving this one