Question 966004
assuming you can use a calculator, then the easiest way to solve this is to convert everything to base 10 that the calculator can handle.


or you can convert everything to base e that the calculator can also handle.


base 10 is LOG function of calculator.


base e is LN function of calculator.


your equation is 2L5(x) = -L2(25)


L5 means log to the base 5.
L2 means log to the base 2


L5(x) = LOG(x)/LOG(5)


L2(25) = LOG(25)/LOG(2)


your problem becomes 2LOG(x)/LOG(5) = -LOG(25)/LOG(2)


solve for LOG(x) to get LOG(x) = LOG(5) * -LOG(25) / LOG(2) / 2


use your calculator to solve for LOG(x) to get LOG(x) = -1.622958091


this is true if and only if 10^-1.622958091 = x


solve for x to get x = .0238254937


that's your answer.


replace x in your original equation and you will see that the equation is true.


your original equation, after it has been converted to base 10, is:


2LOG(x)/LOG(5) = -LOG(25)/LOG(2)


replace x with .0238254937 and the eqution becomes:


2LOG(.0238254937)/LOG(5) = -LOG(25)/LOG(2)


solve this equation using your calculator and you will get:


-4.64385619 = -4.64385619, which is true.


the solution looks good.