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

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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) About Me  (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) About Me  (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



%280.2%2A10%29%5Ex+=+%28%286.4%2A10%5E-1%29%2F%288.0%2A10%5E-2%29%29+ Divide 1.8%2F9.0 to get 0.2. Also, divide 10%5E-3%2F10%5E-4 to get 10%5E-3%2F10%5E-4=10%5E%28-3-%28-4%29%29=10%5E%28-3%2B4%29=10%5E1=10




2%5Ex+=+%28%286.4%2A10%5E-1%29%2F%288.0%2A10%5E-2%29%29+ Multiply 0.2 and 10 to get 2



2%5Ex+=+%280.8%2A10%29+ Divide 6.4%2F8.0 to get 0.8. Also, divide 10%5E-1%2F10%5E-2 to get 10%5E-1%2F10%5E-2=10%5E%28-1-%28-2%29%29=10%5E%28-1%2B2%29=10%5E1=10



2%5Ex+=+8+ Multiply 0.8 and 10 to get 8


log%2810%2C%282%5Ex%29%29+=+log%2810%2C%288%29%29+ Take the log of both sides


x%2Alog%2810%2C%282%29%29+=+log%2810%2C%288%29%29+ Rewrite the left side using the identity log%28b%2Cx%5Ey%29=y%2Alog%28b%2Cx%29}


x+=+log%2810%2C%288%29%29%2Flog%2810%2C%282%29%29+ Divide both sides by log%2810%2C%282%29%29 to isolate x


So after using a calculator, we get this:

x+=+3+


note: you could also ask yourself: 2 to what power equals 8? Since 2%5E3=8 the answer is x=3