Logs
Solve for x
log_2x=5
What is 32
First, another way to write this is 2^5=x. from here you just solve for x so 2x2= 4x2= 8x2= 16x2= 32
Simplify the following expression.
(4xy^2)^0
What is 1
In the end, you need to raise it over to the power of zero which anything to the power of zero is 1.
Find the following number in standard form.
7.28*10^6
What is 7,280,000
To solve this you need to move the decimal 6 times to the right. You do this because 10 is to the power of positive 6. The positive is the direction to the right and the 6 is the amount of movement.
What does PEMDAS stand for?
What is Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction
Solve for x
lne^11=x
What is 11
To find the answer you first move the 11 to the front because e is raised to the power of it. Then you can change it to e^x=e^11 because ln gives you the bases of e. Then you can find that x equals 11.
Also, lne=1 so you are left with 11*1=x which is 11.
Simplify the following expression.
x^8*x^-10*x^4*x^-6
What is
x^-4
When you multiply variables with exponents you need to add the exponents. So 8-10=-2 +4 which equals 2 then 2-6= -4.
Find the following number in standard form.
2.5*10^-3
What is .0025
To solve this you need to move the decimal 3 times to the left. You do this because 10 is to the power of negative 3. The negative is the direction to the left and the 3 is the amount of movement.
What are the top and bottom variables in a fraction called?
What are the denominator and numerator.
Simplify the following
log_3 6+log_3 7
What is
log_3 42
When adding two logs with the same base you multiply the argument. In this case, it's 6*7=42 and keeps the same base.
Simplify the following expression.
(7x^4y^3z)^2
What is
49x^8y^6z^2
You would first distribute the exponent 2 to the whole number 7 and solve for 7^2 which equals 49. Then you would just distribute the 2 to the rest exponents by multiplying them. This is how you get 8, 6, and 2 for the answer.
Find the following number in scientific notation.
800*60,000
What is
4.8*10^7
To find this you need to first multiply the number which gets you 48,000,000. Then you need to move the decimal enough spaces to make the number be between 1 and 10. In this problem, you need to move it to make the number 4.8 and also count how many times it's moved. Here it's moved seven times to the left so the exponent over 10 would be positive 7.
What does anything to the power of zero equal?
What is 1
Simplify the following
4log_8 3-log_8 6
What is
log_8 (27/2)
To find the answer you have to bring the 4 in the front and make it an exponent of 3. Then you simplify 3^4 which gets you 81.
When subtracting logs with the same base you divide the arguments. In this case, you have 81/6 which can be simplified to 27/2 by dividing both the top and bottom by 3.
Simplify with no negative exponents remaining.
(e^2a^-7b^3d^-4) /( e^0a^-4b^-5c^6
What is
(e^2b^8) / (a^3c^6d^4)
When you divide a variable with an exponent you subtract the exponents. So in this case for e, it's 2-0 which gives you e^2.
For a it's -7+4 and you get a^-3 because subtracting by a negative 4 is just adding. Then you would put it in the denominator to make the exponent positive.
For b it's 3+5 and you get b^8.
For c it stays the same as there is only one so c^6 in the denominator.
For d you just need to move it to the denominator to make it positive.
Find the following number in scientific notation.
(8*10^7)/(2*10^-2)
What is
4*10^9
To find this you need to use exponent properties. For the 8 and 2, you treat them like normal numbers and just divide them getting the 4.
Then for the exponent when dividing them you subtract them so 7- (-2)=9 because 2 negative equals a positive so 7+2. Then you just combine this and the 4 to get the answer.
What are the first 5 digits in pie?
What is 3.1415
Simplify the following
3log_2 5-log_2 5+ log_2 4
What is
log_2 100
To find the answer first you make the 3 an exponent on 5 and simplify it to 125.
Then you subtract the first two logs which are
log_2 125 - log_2 5
To do this you divide the arguments 125/5 which equals 25 and then you add the last two logs.
log_2 25 + log_2 4
To simplify this you just multiply 25*4=100 and keep the same base getting you the answer.
Simplify with no negative exponents remaining.
(x^5/y^6)^7*(y^8/x^9)^10
What is
y^38/x^55
The first thing we do is distribute the exponents outside the parenthesis. When an exponent is raised to a power you just multiply and exponents inside by the exponent outside the parenthesis.
This would then get you x^35/ y^42 because 5*7=35 and 6*7=4
You do the same with the 10 and you get y^80/x^90.
Then you combine the 2 fractions and from there you divide x^35 y^80/ x^90 y^42. To do this you just subtract the numerator by the denominator.
For x you get 35-90= -55 so you put it in the denominator to make it positive.
For y you get 80-42=38 and it's positive so you keep it in the numerator as y^38.
Find the following number in scientific notation.
(7*10^-3)(5*10^9)
What is
3.5*10^7
To find this you need to use exponent properties.
For the 7 and 5, you treat them like normal numbers and multiply them getting 35.
Then when multiplying exponent you just add them so it would be -3+9 which equals 6.
When you put this together you get
35*10^6
From here you still need to make b or 35 into a number between 1 and 10. To do this you move the decimal one more time to the left making it 3.5 and then add 1 more exponent making it 7
What is the quadratic formula?
What is
(-b+-sqrt(b^2-4ac))/(2a)=x