Question

Log(2)5+log(2) 1,6 helpppppppppppppp0 вычислите log (3)81, Log(4)log(2)16

Answer 1

Ответ:

1) 3;   2) 4;   3) 1.

Пошаговое объяснение:

Вычислить

$1) log{_2}5+log{_2}1,6;\\2)log{_3}81;\\3)log{_4}log{_2}16.$

Воспользуемся свойствами логарифма

$1) log{_a}b+log{_a}c=log{_a}(b\cdot c);\\a > 0,a\neq 1,b > 0,c > 0$

$2) log{_a}b^{n} =n\cdot log{_a}b;\\a > 0, a\neq 1,b > 0$

$3)log{_a}a=1;\\a > 0,a\neq 1$

Тогда получим

$1) log{_2}5+log{_2}1,6=log{_2}(5\cdot 1,6)=log{_2}8=log{_2}2^{3} =3\cdot log{_2}2=3\cdot1 =3.$

$2)log{_3}81=log{_3}3^{4} =4\cdot log{_3}3=4\cdot 1 =4 .$

$3) log{_4}log{_2}16=log{_4}log{_2}2^{4} =log{_4}(4\cdot log {_2}2)=log{_4}(4\cdot1) =log{_4}4=1.$

#SPJ5

Answer 2

Sure, let's calculate the given logarithmic expressions step by step:

1. log(2)5 + log(2)1.6: We can use the property of logarithms that states: log(a) + log(b) = log(a * b)

So, log(2)5 + log(2)1.6 = log(2)(5 * 1.6)

Now, calculate 5 * 1.6 = 8

So, log(2)5 + log(2)1.6 = log(2)8

Now, we can rewrite this in a different base using the change of base formula:

log(2)8 = log(10)8 / log(10)2

Using a calculator, we get:

log(2)8 ≈ 3

2. log(3)81: This is asking for the logarithm of 81 in base 3.

So, log(3)81 = log(81) / log(3)

Using a calculator, we get:

log(3)81 ≈ 4

3. Log(4)log(2)16: This is asking for the logarithm of 16 in base 2, and then that result in base 4.

First, find log(2)16:

log(2)16 = log(16) / log(2)

Using a calculator:

log(2)16 = 4

Now, find log(4)4:

This is asking for the logarithm of 4 in base 4, which is 1.

So, Log(4)log(2)16 = Log(4)4 = 1

I hope that helps! If you have any more questions or need further clarification, feel free to ask.