5. What is the value of (log 5)³ + (log 20)3 + (log 8) (log 0,25) where log denotes the base-ten logarithm?

The two other forms of this number in accordance with the example given would be 632 thousandths 632 × 1/1000.

Answered by Kalahira | 2024-06-11

The number 0.632 can be expressed as 1000 632 ​ in fraction form and as 6.32 × 1 0 − 1 in scientific notation. These representations demonstrate both its fractional and scientific notation formats. Each form highlights a different aspect of the number's value.
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Answered by Kalahira | 2024-09-04

Jawab:[tex]\boxed{2}[/tex]Penjelasan dengan langkah-langkah:The expression:[tex](\log 5)^3 + (\log 20)^3 + (\log 8)(\log 0.25)[/tex]define a variable for [tex]\log 2[/tex]:assume:[tex]\log 2 = x \Rightarrow \log 5 = \log(10) - \log(2) = 1 - x[/tex]Express all logs in terms of x:[tex]\log 5 = 1 - x\\\log 20 = \log(2^2 \cdot 5) = \log 4 + \log 5 = 2x + (1 - x) = 1 + x\\\log 8 = \log(2^3) = 3x\\\log 0.25 = \log(1/4) = \log(2^{-2}) = -2x[/tex]Substitute into the expression:[tex](\log 5)^3 + (\log 20)^3 + (\log 8)(\log 0.25)[/tex]becomes:[tex](1 - x)^3 + (1 + x)^3 + (3x)(-2x)[/tex]Now compute each term:[tex]1. (1 - x)^3 = 1 - 3x + 3x^2 - x^32. (1 + x)^3 = 1 + 3x + 3x^2 + x^33. 3x \cdot (-2x) = -6x^2[/tex]Add them all:[tex](1 - 3x + 3x^2 - x^3) + (1 + 3x + 3x^2 + x^3) + (-6x^2)[/tex]Group like terms:[tex]Constants: $1 + 1 = 2\\Linear terms: -3x + 3x = 0\\Quadratic terms: 3x^2 + 3x^2 - 6x^2 = 0\\Cubic terms: -x^3 + x^3 = 0[/tex]Answer:[tex]\boxed{2}[/tex]

Answered by Sunariyadi | 2025-07-10