Properties of Logarithms (evaluate)

Question

use $\log 4= 0.602$ and $\log 12=1.079$ to evaluate the logarithm

1. $\log 3$

I'm very confused on how I will evaluate this one I've tried other things but I'm not sure

Answer 1

$\log(12) - \log(4) = \log\left(\frac{12}{4}\right) = \log(3)$

Answer 2

$$\log(b/a) = \log(b) - \log(a)$$ $3=\frac {12}{4}$ implies $\log(3) = \log(12)-\log(4)$

Answer 3

Are you familiar with the logarithm property $log(\frac ab) = log(a) - log(b)$? If not, here's a proof https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/a/justifying-the-logarithm-properties. Now that you know how it works, apply the rule. We know the quanitities of $log(12)$ and $log(4)$ and we need to find $log(3)$. We can see that $3 = \frac{12}4$, so we can try to use our quotient rule. We get $log(3) =log(\frac{12}{4}) = log(12) - log(4) = 1.079 - .602 = .477$. Thus, $log(3) = .477$.