SOLUTION: 8.9=(2/3)log (E/.007^9)

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Question 883945: 8.9=(2/3)log (E/.007^9)
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your equation is:

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.