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

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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))...Show more

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...Show more

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...Show more