Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.

QUESTION

What is log(5*8) equal to?

log(5*8) = 2log(2)+1 ~~ 1.60206

If x, y > 0 then:

log(xy) = log(x)+log(y)

(This follows from 10^(a+b) = 10^a * 10^b and the definition of common logarithms)

color(white)() In general for any valid base b (i.e. b > 0 and b != 1) we also have:

log_b b = 1

(This follows from b^1 = b and the definition of logarithms in general)

So in particular, for common (i.e. base 10) logarithms we have:

log 10 = 1

color(white)() It is also useful to know that:

log 2 ~~ 0.30103

This is a very good approximation. The actual value is nearer 0.301029995664

color(white)() Putting this all together, we find:

log(5*8) = log(2*2*10)

color(white)(log(5*8)) = log(2)+log(2)+log(10)

color(white)(log(5*8)) = 2log(2)+1

color(white)(log(5*8)) ~~ 2*0.30103+1 = 1.60206