Question 896299
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