Question

Question #c8320

Answer 1

`log(0.01^2/x^3) = -10.64`
I assume that `log` means the logarithm with base `10`.

By the property `log(a/b)=log(a)-log(b)` we get:
`log(0.01^2) - log(x^3) = -10.64`
`log((10^{-2})^2) +10.64=log(x^3)`
`log(10^{-4}) +10.64=log(x^3)`
By the property `log(a^b) =b log(a)`
`-4 log(10) +10.64=3 log(x)`
`-4 +10.64=3 log(x)`
`6.64=3 log(x)`
`6.64/3=log(x)`
By definition of logarithm with base `10`
`x=10^{6.64/3} approx 163,43`