SOLUTION: log(base5)2=log(base3)m-log(base3)n

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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