I'm suppose to solve a problem that goes like this.
The graph for the following function f given by $f(x) = 115.82 \cdot 0.94^x + 5$, with $x \geq 5$, gives the temperature of the water after it's been placed in the fridge. Find by calculation what time period the temperature is above 60. Now for me, it appears that the solution is the inequality shown in the picture above.
$115.82 \cdot 0.94^x + 5 > 60$
If I solve this I get
$x > 12.04$
It should be less than that. Not greater. Does taking the log on both sides require one to flip the thingy thing?
$\begin{aligned} 115.82 \cdot 0.94^x + 5 &> 60 \\ \frac{115.82 \cdot 0.94^x}{115.82} &> \frac{55}{115.82} \\ 0.94^x &> \frac{55}{115.82} \\ \log{0.94^x} &> \log{\frac{55}{115.82}} \\ x \cdot \log{0.94} &> \log{\frac{55}{115.82}} \\ x &> \frac{\log \frac{55}{115.82}}{\log 0.94} \\ \end{aligned}$