Question

If the geometric mean of two +ve numbers a and b is 10, then logz+logb=??

what does geometric mean mean?

@phi @ganeshie8

Answer 1

geometric mean comes from
a,b,c having a common ratio
\[ \frac{a}{b} = \frac{b}{c} \]
if you cross multiply you get
\[ b^2 = a c \\ b= \sqrt{ac}\]
in your case

you have
\[ \sqrt{a b} = 10 \]

Answer 2

in other words, you have a G.P. a, 10, b
with a common ratio of
a/10 (or 10/b)

Answer 3

what does geometric mean mean?...

Answer 4

First, it means what I posted up above.

It probably comes from similar right triangles (this is an aside)