Try both methods. Which seems more efficient for you?
See solution.
Practice makes perfect
We are given the logarithmic inequality shown below.
log_5 x < 2
We will show how to solve it graphically and algebraically. Then, we will discuss which method is more efficient in this case.
Solving the Inequality Graphically
To solve a logarithmic inequality graphically, we can graph both sides of the inequality to see for which x-values it gets satisfied.
As we can see, the graphs intersect when x=25. Therefore, the graph of log_5 x is below the graph of y=2 when 0
Solving the Inequality Algebraically
To solve the inequality algebraically, we first need to solve the related equation.
log_5 x = 2
Let's give it a try.
Therefore, x=25 is a critical value. It separates the solutions set from the rest of the x-values. Since a logarithmic function is always increasing, we can know that the values 0
Conclusions
Even thought preferences may vary, for this particular case graphing is simpler and faster, since the boundary point has an integer x-value.
