Tutor profile: Krystal S.

Why is cramming for an exam never a good idea?

We've all heard this before, and you might say "But I do my best under pressure!" To truly understand why cramming doesn't work, or if it does it all goes out of your head after the exam, you need to understand how our brains work. The short explanation is that we need to find ways to move the information we need to learn from our short term memory into our long term memory, and doing this requires retrieval and repetition. I'd love to explain this more in a session with you, so please reach out to me if you want help developing better study habits!

If 3x = 6x - 15, then what does x + 8 equal?

The first thing that needs to be done is to figure out what x equals in the original equation provided. The first step is to move all of the terms with x in it to one side of the equation. I'll move the 6x over with the 3x, which means 6x will need to be subtracted from both sides of the equation. This leaves us with: -3x = -15 Now you need to divide each side of the equation by the coefficient in front of x to get isolate the variable. Don't forget that in this case it is a negative 3 so we must divide by negative so that our x remains positive. Doing this leads to: x = 5 (5 is positive because we divided a negative number by another negative number) You're not done yet! Remember, the problem is not asking you to solve x. It's really asking you to determine what x + 8 equals. So now that we know x is 5, we can plug that in to get 13 as the final answer because: x + 8 = 5 + 8 = 13

Solve for x in the following equation: log(6x) - log(4-x) = log(3)

To solve this problem, you must know the various rules of logarithms. In this case, the Quotient Rule will need to be used. Essentially this rule tells us to convert subtraction of logarithms into division, so your first step would look like this: \log{\left(\frac{6x}{4-x}\right)}=log(3) Now that there is only one log on each side of the equation and they both have the same base (in this case, 10), the Equality Rule can be applied. This allows us to remove the logs and just focus on the rest of the information. So we get: \frac{6x}{4-x}=3 Now we can begin solving an equation you should be more familiar with. No one likes fractions, so let's tackle that first and get something to work with that will make us feel more comfortable. We can remove the fraction by multiplying both sides of the equation by the denominator because remember, what we do to one side of the equation we also have to do to the other side. Multiplying the fraction by 4-x will eliminate the fraction and will leave us with this: 6x = 3(4-x) Now, distribute the 3 to each term inside of the parenthesis to get this: 6x = 12 - 3x Next, we want to get x by itself so we first need to get all terms with x together. To do this we need to add 3x to each side of the equation. This will give: 9x = 12 Now divide by 9 to get x by itself and reduce if necessary. x=\frac{12}{9} 12 and 9 can both be divided by 3, which will reduce our answer to: x=\frac{4}{3} You're not done yet though! The last thing you need to do is plug the answer you got into the original equation to make sure you don't end up with a zero or negative number. You cannot get the logarithm of either of those, so it would be "No solution" in that case. When you check your work though, you'll see that our final solution is correct.