SOLUTION: Please help! I need to be able to do this type of problem for my Chemistry II class and its been a little while since I've had this type of math... ((1.8*10^-3)/(9.0*10^-4))^X

SOLUTION: Please help! I need to be able to do this type of problem for my Chemistry II class and its been a little while since I've had this type of math... ((1.810^-3)/(9.010^-4))^X

Question 121224This question is from textbook Beginning and Intermediate Algebra
: Please help! I need to be able to do this type of problem for my Chemistry II class and its been a little while since I've had this type of math...

((1.8*10^-3)/(9.0*10^-4))^X = ((6.4*10^-1)/(8.0*10^-2))
In case this is confusing the way it is written out, on the left side of the equation the entire division problem is raised to the power of x.
I know this is a quadratic problem, where I have to get to ax^2 + bx + c = 0, then go on and plug the numbers into the quadratic formula. I'm having trouble getting it into this form though. The professor said that the final answer is 3, but I havent been able to get that on my own. I'd appreciate if anyone could give me a step-by-step explanation of how to do this, so that I can go on to do the other similar problems on my own. Thanks a lot! This question is from textbook Beginning and Intermediate Algebra

Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
this is not a quadratic problem, it is exponents/logarithms

performing the operations in the parentheses gives (2)^X=(8)

2 cubed is 8, so X=3

for future reference (in case the numbers are not so straight forward)
__ taking the log gives X(log(2))=log(8), so X=(log(2))/log(8)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Well in this case, you do not need the quadratic formula.

Start with the given equation

Divide to get . Also, divide to get

Multiply 0.2 and 10 to get 2

Divide to get . Also, divide to get

Multiply 0.8 and 10 to get 8

Take the log of both sides

Rewrite the left side using the identity }

Divide both sides by to isolate x

So after using a calculator, we get this:

note: you could also ask yourself: 2 to what power equals 8? Since the answer is
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