The domain:The number of which the logarithm is taken must be greater than 0.
The base of the logarithm must be greater than 0 and not equal to 1.
* greater than 0:
*not equal to 1:
Sum up all the domain restrictions:
The solution:
Now if the base of the logarithm is less than 1, then you need to flip the sign when solving the inequality. If it's greater than 1, the sign remains the same.
* if the base is less than 1:
The inequality:
* if the base is greater than 1:
The inequality:
![\log_{8x^2-23x+15} (2x-2) \leq \log_{8x^2-23x+15} 1 \ \ \ \ \ \ \ |\hbox{the sign remains the same} \\ 2x-2 \leq 1 \\ 2x \leq 3 \\ x \leq \frac{3}{2} \\ x \leq 1 \frac{1}{2} \\ x \in (-\infty, 1 \frac{1}{2}] \\ \\ \hbox{including the condition that the base is greater than 1:} \\ x \in (-\infty, 1 \frac{1}{2}] \ \land \ x \in (2, \infty) \\ \Downarrow \\ x \in \emptyset](https://tex.z-dn.net/?f=%5Clog_%7B8x%5E2-23x%2B15%7D%20%282x-2%29%20%5Cleq%20%5Clog_%7B8x%5E2-23x%2B15%7D%201%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%7C%5Chbox%7Bthe%20sign%20remains%20the%20same%7D%20%5C%5C%202x-2%20%5Cleq%201%20%5C%5C%202x%20%5Cleq%203%20%5C%5C%20x%20%5Cleq%20%5Cfrac%7B3%7D%7B2%7D%20%5C%5C%20x%20%5Cleq%201%20%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%20x%20%5Cin%20%28-%5Cinfty%2C%201%20%5Cfrac%7B1%7D%7B2%7D%5D%20%5C%5C%20%5C%5C%20%5Chbox%7Bincluding%20the%20condition%20that%20the%20base%20is%20greater%20than%201%3A%7D%20%5C%5C%20x%20%5Cin%20%28-%5Cinfty%2C%201%20%5Cfrac%7B1%7D%7B2%7D%5D%20%5C%20%5Cland%20%5C%20x%20%5Cin%20%282%2C%20%5Cinfty%29%20%5C%5C%20%5CDownarrow%20%5C%5C%20x%20%5Cin%20%5Cemptyset)
Sum up both solutions:
The final answer is:
Answer:
x+19=19+x
Step-by-step explanation:
Answer: 10:55
Step-by-step explanation:
Taking statement at face value and the simplest scenario that commencing from 08:00am the buses take a route from depot that returns bus A to depot at 25min intervals while Bus B returns at 35min intervals.
The time the buses will be back at the depot simultaneously will be when:
N(a) * 25mins = N(b) * 35mins
Therefore, when N(b) * 35 is divisible by 25 where N(a) and N(b) are integers.
Multiples of 25 (Bus A) = 25, 50, 75, 100, 125, 150, 175, 200 etc
Multiples of 35 (Bus B) = 35, 70, 105, 140, 175, 210, 245 etc
This shows that after 7 circuits by BUS A and 5 circuits by Bus B, there will be an equal number which is 175 minutes.
So both buses are next at Depot together after 175minutes (2hr 55min) on the clock that is
at 08:00 + 2:55 = 10:55
Answer:
Step-by-step explanation:
Volume of a rectangular pyramid is given as = 
Where,
Plug in the above values into the formula for volume of rectangular pyramid:
Volume of the rectangular pyramid =
