logs and powers questions

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March 21st 2011, 06:11 AM
Lia85

logs and powers questions

Hi I'm new here. Unfortunately I dont have the time to make an official introduction, since I've been scratching my head over some assignments for the past three days and now I only have two hours left to do them.

I'd be really grateful if someone could help me with the following (listed from easiest to most difficult):

1) 2,2= -log(c), 2,2= pH value and c= molar concentration.

What is c in the above equation?

If the molar concentration in a liquid is multiplied by 100, the pH will be reduced by 2. Explain why (something to do with logarithmic rules).

2) f(x)= 225.027* x^ -0.5

- What is x when f(x) is 10.000?
- By which percent-rate will x increase if y decreases with 5 %

Now they're not that difficult, but I think the reason I can't seem to solve them is because I'm not sure if the reverse function of a negative power in this case x^-0.5, is 1/sqr(-0.5). When I try to isolate x, it certainly doesn't work to use 1/sqr(-0.5) in the process. Nor does it help when I try to use it to calculate the percent rate increase in x, for which the formula is: 1+ry= (1+rx)^a, rx= percent rate for x, ry= percent rate for y.

Please help ASAP!

Thank you in advance.
March 21st 2011, 06:41 AM
HallsofIvy

Quote:

Originally Posted by Lia85

Hi I'm new here. Unfortunately I dont have the time to make an official introduction, since I've been scratching my head over some assignments for the past three days and now I only have two hours left to do them.

I'd be really grateful if someone could help me with the following (listed from easiest to most difficult):

1) 2,2= -log(c), 2,2= pH value and c= molar concentration.

What is c in the above equation?

The "inverse" of log (base 10) is 10 to a power. Write that as log(c)= -2.2 and take $10^{log(c)}= 10^{-2.2}$ .

Quote:

If the molar concentration in a liquid is multiplied by 100, the pH will be reduced by 2. Explain why (something to do with logarithmic rules).

100= 10^2 so that log(100)= 2.

Quote:

2) f(x)= 225.027* x^ -0.5

- What is x when f(x) is 10.000?

That's the same as $\frac{225.027}{\sqrt{x}}= 10.00$ or $\sqrt{x}= \frac{10}{225.027}$

Quote:

- By which percent-rate will x increase if y decreases with 5 %

Do you mean y= f(x)? 10.000 decreased by 5% will be 9.500. Solve the same equation with 9.5 instead of 10 to get the new value of x. The percentage increase will be "(new x- old x)/old x.

Quote:

[Now they're not that difficult, but I think the reason I can't seem to solve them is because I'm not sure if the reverse function of a negative power in this case x^-0.5, is 1/sqr(-0.5).

NO, it is just 1/sqrt(0.5). The negative power puts the square root in the denominator but does not change a sign.

Quote:

When I try to isolate x, it certainly doesn't work to use 1/sqr(-0.5) in the process. Nor does it help when I try to use it to calculate the percent rate increase in x, for which the formula is: 1+ry= (1+rx)^a, rx= percent rate for x, ry= percent rate for y.

Please help ASAP!

Thank you in advance.
March 21st 2011, 06:53 AM
Lia85

Hi HallsosIvy and thank you for your quick reply.

"Do you mean y= f(x)? 10.000 decreased by 5% will be 9.500. Solve the same equation with 9.5 instead of 10 to get the new value of x. The percentage increase will be "(new x- old x)/old x. "

Yes I know this, but because this is a power function, we have to use this formula 1+ry= (1+rx)^a, rx= percent rate for x, ry= percent rate for y, in order to explain the relative increment in x (i.e. the percent rate by which it increases when y decreases). And when I try this I get awfully weird numbers (that I didn't even know existed), because I can't seem to properly isolate rx in that equation (it should be a bumber between one and zero).

Again thank you :)
March 21st 2011, 06:57 AM
Lia85

nvm