Question 883945
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 <a href = "http://www.alcula.com/calculators/scientific-calculator/" target = "_blank">***** ALCULA *****</a>


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.


<img src = "http://theo.x10hosting.com/2014/jun2402.jpg" alt = "$$$" </a>