8.9 = (2/3) * log(E / .007^9)
since log(E / .007^9) = log(E) - log(.007^9), your equation becomes:
8.9 = (2/3) * [ log(E) - log(.007^9) ]
simplify this to get:
8.9 = (2/3) * log(E) - (2/3) * log(.007^9)
add (2/3) * log(.007^9) to both sides of this equation to get:
8.9 + (2/3) * log(.007^9) = (2/3) * log(E)
divide both sides of this equation by (2/3) to get:
(8.9 + (2/3) * log(.007^9) / (2/3) = log(E)
solve for log(E) to get:
log(E) = -6.04411764
since y = log(x) if and only if 10^x = y, then:
let x = E and y = -6.04411764 and you get:
10^(-6.04411764) = E which means that E = 9.034047301 * 10^-7.
that should be your answer.
replace E in your original equation with that and the equation should be true.
i did and i got 8.9 = 8.9 which confirms that the answer is correct.
the following picture shows the progression using the online scientific calculator by ***** ALCULA *****
here's the picture:
in the picture, the underlined numbers on the left are the index to ans(x) where x = 0 to 3.
you got:
ans(1) = log(E)
ans(2) = E
ans(3) = 8.9 which confirms the answer is correct.
