Question

Log5 12-2log5 2/log5 18+log5 0,5​

Answer 1

Ответ:

1/2

Объяснение:

(log5 12-log5 4)/(log5 (18*0,5))=log5 3/log5 3^2=

=log5 3/(2*log5 3)=1/2

Answer 2

Let's break down the expression step by step:

log5 12 - 2log5 2 / log5 18 + log5 0.5

First, let's simplify the expression within the logarithms:

log5 12 = log5 (2 * 2 * 3) = log5 2 + log5 2 + log5 3

log5 2 / log5 18 = log5 (2 / 18) = log5 (1 / 9) = log5 (1) - log5 (9) = 0 - log5 9

log5 0.5 = log5 (1 / 2) = log5 1 - log5 2 = 0 - log5 2

Substituting these simplified expressions back into the original expression:

(log5 2 + log5 2 + log5 3) - 2(log5 2 / log5 18) + log5 0.5

(log5 2 + log5 2 + log5 3) - 2(0 - log5 9) + (0 - log5 2)

(log5 2 + log5 2 + log5 3) + 2log5 9 + log5 2

Now, we can combine the logarithms using the properties of logarithms:

log5 2 + log5 2 + log5 3 + 2log5 9 + log5 2

= log5 (2 * 2 * 3) + log5 (9^2) + log5 2

= log5 (12) + log5 (81) + log5 2

= log5 (12 * 81 * 2)

= log5 (1944)

So, the simplified expression is log5 (1944).