Question

2log4(8)-3log8(4)+log2(32)+18

Answer 1

Ответ:равно 21.7958800173

Answer 2

2log4(8)=2log2^2(2^3)=2*3/2=3. 3log8(4)=3log2^3(2^2)=3*2/3=2. Log2(32)=log2(2^5)=5. Итог:3-2+5+18=24

Answer 3

To simplify the expression 2log₄(8) - 3log₈(4) + log₂(32) + 18, we can use logarithm properties and simplify each term step by step.

1. Start with the first term: 2log₄(8).

   We know that 8 is 2^3, so log₄(8) = log₄(2^3).

   Now, we can use the property that logₐ(b^c) = c * logₐ(b):

   2log₄(2^3) = 2 * 3 * log₄(2).

   Since log₄(2) is a common logarithm value, we'll leave it as it is for now.

   So, the first term becomes: 6 * log₄(2).

2. Move on to the second term: -3log₈(4).

   We know that 4 is 2^2, so log₈(4) = log₈(2^2).

   Using the same property as before:

   -3log₈(2^2) = -3 * 2 * log₈(2).

   So, the second term becomes: -6 * log₈(2).

3. The third term is log₂(32).

   We know that 32 is 2^5, so log₂(32) = log₂(2^5).

   Using the property again:

   log₂(2^5) = 5 * log₂(2).

   The third term becomes: 5 * log₂(2).

4. Now, combine the simplified terms:

   6 * log₄(2) - 6 * log₈(2) + 5 * log₂(2) + 18.

5. Logarithm property: logₐ(a) = 1 for any positive number a.

   So, we can simplify further:

   6 * 1 - 6 * 1 + 5 * 1 + 18 = 6 - 6 + 5 + 18 = 23.

So, the simplified expression is 23.