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Pproximate the logarithm using the properties of logarithms, given

log _b (2)≈0.3562, log _b (3)≈0.5646, and
log b​(5)≈0.8271. log (
(0.25) is approximately:

User Epicrato
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Final answer:

To approximate the logarithm of 0.25 using properties of logarithms, we can use the property log(b)(a/b) = log(b)(a) - log(b)(b) and manipulate the given logarithms to find log(b)(0.25) as -0.7124.

Step-by-step explanation:

To approximate the logarithm of 0.25, we can use the property of logarithms that states logb(a/b) = logb(a) - logb(b). Using this property, we can write log(b)(0.25) as log(b)(1/4), which can be simplified as log(b)(1) - log(b)(4). Since log(b)(1) = 0, we can find log(b)(4) by manipulating the given logarithms. We have log(b)(4) = log(b)(2 * 2) = log(b)(2) + log(b)(2).

Using the values given, we can substitute log(b)(2) as 0.3562. Therefore, log(b)(4) = 0.3562 + 0.3562 = 2 * 0.3562 = 0.7124. Finally, using log(b)(1) = 0 and log(b)(4) = 0.7124, we can calculate log(b)(0.25) as log(b)(1) - log(b)(4) = 0 - 0.7124 = -0.7124.

We can approximate the given logarithm using the properties of logarithms. We have the values logb(2) ≈ 0.3562, logb(3) ≈ 0.5646, and logb(5) ≈ 0.8271. The provided logarithm is logb(0.25), which can be rewritten as logb(1/4) or logb(2-2). Using the properties of logarithms, we can say logb(2-2) is the same as -2 × logb(2). Substituting the known value, we get -2 × 0.3562 = -0.7124 as the approximation of logb(0.25).

User Moien Tajik
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