How do you solve this equation? Does it contain log?

log(√b / 1000a)

= log(√b) - log(1000a)

= 1/2 * log(b) - log(1000) - log(a)

= -1.2 - 0.16 - log(1000)

= - (1.36 + log(1000))

log a=0.16 and log b=-2.4. Find log ((sqrt(b))/(1000a)). After I expand it I'm not sure if it's a full number or if it contains log

a = 10^0.16

b = 10^2.4

sqrt b = 10^1.2

1000a = 10^3 * 10^0.16 = 10^3.16

(sqrt(b) /(1000a) = 10^1.2 / 10^3.16

(sqrt(b) /(1000a) = 10^(1.2-3.16)

(sqrt(b) /(1000a) = 10^-1.96

Log 10^-1.96 = -1.96

What base are you using for the logarithms?

Let's say the base is x, therefore:

a = x^0.16

b = x^(-2.4)

Therefore:

log (sqrt(b) / (1000a))

= log (sqrt(x^(-2.4)) / (1000x^0.16))

= log(x^(-1.2) / (1000x^0.16))

= log(x^(-1.2 - 0.16) / 1000)

= log(x^(-1.36) / 1000)

= -1.36 - log(1000)

If x = 10, we have:

= -1.36 - 3

= -4.36