Logs & Square roots

Question 1

When dealing with Negative logs:
What is a shortcut to solving a problem like

-log(1*10⁻²) = ?

Answer 1

When dealing with negative Logs and a number in scientific notation

*preferbaly a 1 multipled by 10ⁿ

We take the exponent sitting on top of the 10 and then change the sign.

So our answer to this problem would be 2

Question 2

When dealing with Negative logs:
What is a shortcut to solving a problem like

-log(3*10⁻²) = ?

Answer 2

When dealing with negative Logs and a number in scientific notation

We take the exponent sitting on top of the 10 and then change the sign.

So our answer to this problem would be 2

HOWEVER, because the 10^-2 is not being multipled by 1 we have to do a little extra steps.

We have to choose a number between ((-n)-1) and (-n)

so in order to do that you should memorize this list of numbers

if the scientifc notation number is multiplied by:

• 3; 0.53 follows after
• 5; 0.3 follows after
• 8; 0.1 follows after

so in this case the answer would be roughly around:

1.53

Question 3

How to aproximate a square root such as :

√123

Answer 3

1. Find the perfect squares that is just below the number given - in this case it would be 11² = 121
2. Then find the perfect square that is just above the number - in this case it would be 12² = 144
3. Now we know the number is between 11 and 12. To get a better estimate pick a decimal according to wether the number is closer to the smaller number or larger.

Question 4

What is the square root of 2?

Answer 4

1.4

Question 5

What is the square root of 3?

Answer 5

1.7

Question 6

What is he square root of 10?

Answer 6

3.1

Question 7

What is the cubed root of 127?

Answer 7

3

Question 8

What is the cubed root of 4 squared?

Answer 8

2.5

Question 9

What is the difference when you round up in a numerator vs rounding up in denominator?

Answer 9

When you round up in a numerator of a problem the actual answer will always be lower than the estimated answer, if you round up in the denominator of a problem the actual answer will be higher than the estimated answer.

Question 10

LARS

Answer 10

When you are adding to the exponent of a number in scientific notation you move the decimal to the left. And if you are subtracting from the exponent than you move decimal to the right.

Ex: if you want to increase the exponent in the number 1.4 x 10² by one (meaning the exponent will be 3). You have to move the decimal one place to the left.

so, it will be: 0.14 x 103

Ex: if you want to decrease the exponent in the number 2.4 x 10⁵ by 3 (meaning the exponent will be 2). You have to move the decimal three places to the right.

so, it will be: 2400 x 10²

Question 11

Adding and subtracting exponents.

Answer 11

When adding or subtracting two numbers in scientific notation that have a difference in exponents greater than the magnitude of 2 (10²) then the answer will be the one with the greater exponent.

Ex: (2.45 x 10^-5) + (3.00 x 10^-15)

|15-5| = 10 > 2

So, answer will be 2.45 x 10^-5