SOLUTION: How do I solve this problem?
Db=10log(5.3x10^-5/10^-16)
Algebra.Com
Question 471160: How do I solve this problem?
Db=10log(5.3x10^-5/10^-16)
Found 2 solutions by Tatiana_Stebko, Theo:
Answer by Tatiana_Stebko(1539) (Show Source): You can put this solution on YOUR website!
If you need more, have to use scientific calculator
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
I think your equation is as follows:
Db = 10*log((5.3 * 10^(-5))/(10^(-16))
Sticking that through the algebra.com formula generator, it would look like:
Db =
Assuming that's your equation, then you would solve it as follows:
Db = is equivalent to:
Db = which is equivalent to:
Db = which is equivalent to:
Db = which you can solve using your calculator to get:
Db = 10*(11.72427587) which equals 117.24237587.
I confirmed by using my calculator to solve the original equation.
Since that gave me the same answer as the final equation, I assumed the translation of the equation was correct.
The laws of logarithms that applied are:
First Law: log(a*b) = log(a) + log(b)
Second Law: log(a/b) = log(a) - log(b)
Third Law: log(a^b) = b*log(a)
In your problem, I could assign letters to each configuration to make it clearer.
Assume 5.3 equals a
Assume 10^(-5) = b
Assume 10^(-16) = c
Your equation then becomes:
Db =
Use second law to get:
Db =
Use first law to get:
Db =
Since b = 10^(-5), we make b = d^e by making d = 10 and e = -5
Since c = 10^(-16), we make c = f^g by making f = 10 and g = -16
Our equation of:
Db = becomes:
Db =
Now we use the third law to get:
Db = becomes:
Db =
That becomes our final equation.
Since:
a = 5.3
e = -5
d = 10
g = -16
f = 10
substituting in our final equation, we get:
Db =
We simplify that to get:
Db =
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