Question 474863: Can't figure how to solve
4 Log10 (4x)=4
please help
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equation is:
4 * log(10,4x) = 4
divide both sides of that equation by 4 to get:
log(10,4x) = 1
note that log(10,4x) is equal to the log of 4x to the base of 10.
you can also call is log(4x), since the base of 10 is implied.
using that notation, your problem equation becomes:
4 * log(4x) = 4
divide both sides of this equation by 4 and you get:
log(4x) = 1
this means that 4x = 10
this is because of the basic definition of logarithms that states:
log(x) = y if and only if 10^y = x
your equation states:
log(4x) = 1
this can be true if and only if 10^1 = 4x
since 10^1 is equal to 10, this means that:
4x = 10
divide both sides of this equation by 4 and you get:
x = 10/4
that's your answer.
plug that in your original equation and you get:
4 * log(4x) = 4 becomes:
4 * log(4*10/4) = 4 which becomes:
4 * log(10) = 4
since the log of 10 is equal to 1, this becomes:
4 * 1 = 4 which is true, confirming that the answer of x = 10/4 is good.
here's a reference that explains the relationship between logs and exponents.
http://www.purplemath.com/modules/logs.htm
This relationship is in the generic form of:
log(b,x) = y if and only if b^y = x
in your problem, the b was equal to 10.
it can be any base, not just 10.
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