Aaaargh! To raise the Richter scale's intensity in one unity, we should multiply the energy released by

Richter scale's intensities range from 0 to 9. They're measured according to the formula

i= ⅔ log₁₀(E/Eo)

i stands for intensity
E is the energy released by the earthquake
Eo=7*10⁻³ kWh

QUESTION- To raise the intensity in one unity, we should multiply the energy by?
a) 10¹°
b) 10³
c) 10√10 <---That's the answer. How to do the calculation??
d) 10√3

i + 1 = (2/3) log(aE/E₀)
(2/3)log(E/E₀) + 1 = (2/3)log(aE/E₀)
(2/3)log(E) - (2/3)log(E₀) + 1 = (2/3)log(a) + (2/3)log(E) - (2/3)log(E₀)
1 = (2/3)log(a)
3/2 = log(a)
a = 10^(3/2) = 10 * 10^(1/2) = 10√10

i= ⅔ log₁₀(E/Eo)
put Eo = 1 (the result is independent from this value)


i = (2/3) log₁₀(E)
we need an energy
log₁₀(E) = 3i/2
E = 10^(3i/2)

if we want an intensity i + 1

(2/3) log₁₀(E') = i + 1
log₁₀(E') = 3i/2 + 3/2
E' = 10^(3i/2 + 3/2)

so the ratio
E'/E = 10^(3i/2 + 3/2)/ 10^(3i/2)
a ratio of powers with the same base is the base raised to the difference of the exponents

E'/E = 10^(3i/2 + 3/2 - 3i/2)
E'/E = 10^(3/2)
= 10 · 10^(1/2) = 10√10

You would have to go to the tenth power, wouldn't you?