Question 966004: 2log5(x)= -log2(25)
Solve for x.
the 5 next to log is small and the 2 next to log is small
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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