**Log(√(10)) + log(0.01)**

explain how to solve without calculator please.

explain how to solve without calculator please.

Since nothing different is shown, we can assume that these logs

are to the base 10.

So the log of a number means:

In order to get that number, what power do you raise 10 to ?

log(√10) = 1/2 . . . . . (10 to the 1/2 power produces √10)

log(0.01) = -2 . . . . . (10 to the -2 power means 1/10² and produces 0.01)

So the sum of those two logs is (1/2) + (-2) = ** -(1 and 1/2) **.

We use the rule : log X^n = n * log X

log 10 = 1 as the base of logarithm is also 10.*log √10 = log (10)^1/2 = 1/2 log 10 = 1/2 * 1 = 1/2**log 0.01 = log 10^-2 = -2 log 10 = - 2 * 1 = -2 **add the two: 1/2 - 2 = -3/2*

==========================================

log 0.01 can be done also as : log 1/100 = log 1 - log 100

= 0 - log 10² = - 2 * log 10 = - 2 * 1 = - 2

here we used log ( X / Y ) = log X - log Y

If your question is not fully disclosed, then try using the search on the site and find other answers on the subject Mathematics.

Find another answersMathematics, published 11.05.2023

Mathematics, published 23.03.2023

Use the equation to identify the center and radius of the circle (X+3)^2+(y-7^2=11

Mathematics, published 27.05.2023