Math: If logb5=a, logb2.5=c, and 5^x=2.5, then x=?

If logb5=a, logb2.5=c, and 5^x=2.5, then x=?

Math: If logb5=a, logb2.5=c, and 5^x=2.5, then x=?
logb5=a


logb2.5=c





5^x=2.5


(logb both side)


logb5^x=logb2.5


x logb5 = logb2.5 (b is any number, i prefer 10)


x = log2.5/log5 = 0.569...





(i think it's 'computer says')
Reply:The equation you have to solve is





5^x = 2.5





and the way to proceed is to take logarithms of both sides :





x * log 5 = log 2.5





so x = log 2.5 / log 5





and it does not matter what base you use for the logarithms - you could use 2, or 10, or e or anything that takes your fancy.





However, since you are given these two logarithms to some unknown base, b, then I presume that you are meant to give the answer in terms of those given logarithms, therefore





x = c / a
Reply:computer says x=log5(2.5)=logb2.5/logb5=c/a..use log base conv rule..