Question 896299: log(base5)2=log(base3)m-log(base3)n
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! log5(2) = log10(2)/log10(5)
log3(m) - log3(n) = log3(m/n)
log3(m/n) = log10(m/n)/log10(3)
log5(2) = log3(m) - log3(n) becomes:
log10(2)/log10(5) = log10(m/n)/log10(3)
solve for log10(m/n) and you get:
log10(m/n) = log10(2) * log10(3) / log10(5)
you can use the log function of your calculator to get:
log10(m/n) = .2054849398
this is true if and only if 10^.2054849398 = m/n
you get m/n = 1.605036599
you can't really solve for m or n.
the best you can do is solve for m in terms of n or n in terms of m.
solving for m in terns of n, we get:
m = 1.605036599 * n
if i did this right, then we can assume any value of n and we should get a true original equation.
i'll pick any value for n at random and see if that holds water.
let n = 15
your original equation is:
log(base5)2=log(base3)m-log(base3)n
i translated this to:
log5(2) = log3(m) - log3(n)
i then translated this to:
log5(2) = log3(m/n)
i then translated this to:
log10(2)/log10(5) = log10(m/n)/log10(3)
we can use this equation to see if we're correct.
we allowed n to be equal to 15.
m is equal to 1.605036599 * 15.
m/n is therefore equal to 1.605036599 * 15 / 15 which makes m/n always equal to 1.605036599 regardless of the value of n.
our equation becomes:
log10(2)/log10(5) = log10(1.605036599)/log10(3)
evaluate both sides of this equation to get:
.4306765581 = .4306765581
looks like we did good.
assuming this is what you wanted, your solution is:
m/n = 1.605036599
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