help with logrithmic math question?

Question

Ok I have this equation

M=(2/3)log(E/10^4.4)

and I need it in terms of E=

thanks.

Answer 1

M=(2/3)(log(E)-log(10^4.4))
so M=(2/3)[log(E)-4.4]
log(E)=(3/2)M+4.4
So E=10^(1.5M+4.4)

Answer 2

All we have to do is try and see what we can to to isolate E, and we must use certain logarithmic properties, which I will describe as I work this problem.

M = (2/3)log(E/10^4.4)

First, we must get rid of the coefficient in front of the log, so that we get it out of the way when we decompose the logarithm:

(3/2)M = log(E/10^4.4)

Now we use a property called the Division Property, which states:

log(a/b) = log(a) - log(b)

(3/2)M = log(E) - log(10^4.4)

Since log is base 10 unless specified, then we can say this:

-log(10^4.4) = -4.4

So we plug that back in:

(3/2)M = log(E) - 4.4

Now we add the 4.4 to isolate the log(E):

(3/2)M + 4.4 = log(E)

Now we must transfer this to an exponential function to isolate E. If you remember, logarithms say:

log(x) = c

The power you put on 10 to get x is c, so in order to make it an exponential, we do exactly what it says and take 10 to the cth power:

x = 10^c

And there we go, now we know how to work it:

(3/2)M + 4.4 = log(E)

10^((3/2)M + 4.4) = E

And there you go.

Answer 3

M = (2/3) log(E/10^4.4)
M = log((E/10^4.4)^(2/3))
10^M = (E/10^4.4)^(2/3)
(10^M)^(3/2) = E / 10^4.4
10^(3M/2)/10^4.4 = E