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### Example 8 Solve the equation: $\frac{ log(x+6) }{ log x} = 2$ **Solution:** Given: $\frac{ log(x+6) }{ log x} = 2$ **Solution:** $log(x+6)=2logx$ $log(x+6)=logx^2$ By equality rule of logarithms: $logm = logn$ $m = n$ $x+6=x^2$ $x^2 - x - 6 = 0$ $(x-3)(x+2) = 0$ Therefore, we get...

### Example 8 Solve the equation: $\frac{ log(x+6) }{ log x} = 2$ **Solution:** Given: $\frac{ log(x+6) }{ log x} = 2$ **Solution:** $log(x+6)=2logx$ $log(x+6)=logx^2$ By equality rule of logarithms: $logm = logn$ $m = n$ $x+6=x^2$ $x^2 - x - 6 = 0$ $(x-3)(x+2) = 0$ Therefore, we get $x=3$ or $x=-2$. Now, log x = log 3 is allowed. However, log x = log(-2) is not allowed because a logarithm of a negative term is not allowed. Therefore, the solution to the equation is **x = 3**.