# Math Help - Logarithm

1. ## Logarithm

One more problem:

Find all $k \in R$ so that inequalities $log_{(x-1)^2}(x+5)^4\geq1$ and $log_{x+k}(x+3)\leq1$ have no mutual solutions.

2. ## Re: Logarithm

Hey darence.

Can you show us what you have tried (Hint: try expanding the definitions using log laws for change of base and powers and get an expression with k on one side of the inequality)?

3. ## Re: Logarithm

That's my biggest problem. I don't know where to start from with this problem

4. ## Re: Logarithm

Hint: log_a(x) = ln(x)/ln(a) [Change of Base Rule] and ln(a^x) = x*ln(a)