I have 2 problems I need help with using either substitution or elimination method what is the solution set of 3x -2y = -4 and 5x = 2y? Second, Given: log sub a 2 = .4, log sub a 3 = .5, log sub a 5 = .8 what is the value of log sub a .01?
On the first, I will gladly critique your work.
Secondly, note that
loga 10= loga 2 + loga5
loga 1 = 0
loga .1= - loga 10
loga .01 = - 2loga 10
the answer is none YOU can get the answer by listening to Radio Disney or playing BIG Brain Accamady On a Nintendo Ds
For the first problem, we have the following system of equations:
1) 3x - 2y = -4
2) 5x = 2y
To solve this system using the substitution method, we can solve equation 2) for y and substitute that into equation 1). Let's start by solving equation 2) for y:
Rearrange equation 2): 5x = 2y
Divide both sides by 2: (5/2)x = y
Now substitute (5/2)x for y in equation 1):
3x - 2(5/2)x = -4
Simplify: 3x - 5x = -4
Combine like terms: -2x = -4
Divide both sides by -2: x = 2
Now substitute the value of x back into equation 2) to find y:
5(2) = 2y
10 = 2y
Divide both sides by 2: 5 = y
Therefore, the solution set for the system of equations is x = 2 and y = 5.
Regarding your request for critique, you did not show any work or steps to solve the problem, so it's difficult to provide specific feedback. Please let me know if you have any questions or need further clarification.
Now, let's move on to the second problem, which involves logarithms. We are given the following logarithmic values:
loga 2 = 0.4
loga 3 = 0.5
loga 5 = 0.8
We need to find the value of loga 0.01. To do this, we can use the properties of logarithms:
1) loga (ab) = loga a + loga b
2) loga (a/b) = loga a - loga b
3) loga (a^n) = n * loga a
Using these properties, we can rewrite loga 0.01 as follows:
loga 0.01 = loga (1/100) = loga 1 - loga 100
Since loga 1 = 0 (by definition), we can simplify further:
loga 0.01 = - loga 100
Now, we can use property 1) mentioned earlier:
loga 100 = loga (10 * 10) = loga 10 + loga 10
Using property 2) again, we know that loga 10 = loga 2 + loga 5:
loga 10 = loga 2 + loga 5
Substituting the given values for loga 2 and loga 5:
loga 10 = 0.4 + 0.8 = 1.2
Finally, we substitute this value back into our previous equation:
loga 0.01 = - loga 100 = - (loga 10 + loga 10) = - (1.2 + 1.2) = -2.4
Thus, the value of loga 0.01 is -2.4.
I hope that clarifies both problems for you. If you have any further questions or need additional explanation, feel free to ask!