&Ifb > 1, log_b x > log_b y if and only if
x > y.
&Ifb > 1, log_b x < log_b y if and only if x < y.
Using this property, we can rewrite the exponential inequality as a logarithmic inequality.
3^(y-1) ≤ 4^y ⇔ log 3^(y-1) ≤ log 4^yTo solve the above logarithmic inequality, we need to recall the Power Property of Logarithms.
Power Property of Logarithms
log_b m^p = p log_b m, where m and b are positive numbers, with b≠1.
The final step to isolate y will be to divide both sides of the inequality by log 4 - log 3. Before we take this step, let's stop for a moment and think about the sign of the expression.
4>3 ⇔ log 4 > log 3
Because log 4 is greater than log 3, we know that the difference between log 4 and log 3 will be a positive number. Therefore, to divide by this value, we mustn't reverse the inequality sign.
