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Evaluate the expression:

(a) \(\log_{25}(25^6 \times 25)\)

(b) 625

(c) \(\log_2(25)\)

(d) 2

Answer :

In this case, the evaluated expressions are:

  • (a) Assuming a multiplication error was present and the corrected expression is logâ‚‚â‚…(25⁶ * 25), the value would be 7.
  • (b) 625
  • (c) logâ‚‚(25) is approximately 4.64386
  • (d) 2

To evaluate the expressions, let's tackle them one by one: (a) log₂₅(25⁶25) It seems there is a formatting error or a missing operator between "25⁶" and "25".

Let's assume that the expression should be the logarithm base 25 of (25 raised to the power of 6) multiplied by 25. In that case, we would have:

log₂₅(25⁶ * 25)

Using properties of logarithms, especially the power rule log_b(a^c) = c * log_b(a), and knowing that log_b(b) = 1 since any number (besides 0) raised to the power of 0 is 1, we can evaluate the expression as follows:

logâ‚‚â‚…(25^7) = 7 * logâ‚‚â‚…(25)

Since 25 is the base of the logarithm: logâ‚‚â‚…(25) = 1

Therefore:

7 * logâ‚‚â‚…(25) = 7 * 1 = 7

The value of this expression, assuming the multiplication between "25⁶" and "25", is 7.

(b) 625 This part of the expression is just a number. There are no operations to perform on it: 625 The value of this expression is 625.

(c) logâ‚‚(25) This part is asking for the logarithm base 2 of 25, which can be evaluated using the change of base formula:

log₂(25) = log₁₀(25) / log₁₀(2)

Using a calculator or the known values of logarithms:

log₁₀(25) ≈ 1.39794 (since 10^1.39794 ≈ 25)

log₁₀(2) ≈ 0.30103 (since 10^0.30103 ≈ 2)

Now we divide the two to find the value:

logâ‚‚(25) ≈ 1.39794 / 0.30103 ≈ 4.64386

So the value of logâ‚‚(25) is approximately 4.64386.

(d) 2 The fourth part of the expression is just the number 2:

2 The value of this expression is 2.

To summarize, the evaluated expressions are:

(a) Assuming a multiplication error was present and the corrected expression is log₂₅(25⁶ * 25), the value would be 7.

(b) 625

(c) logâ‚‚(25) is approximately 4.64386

(d) 2

Thank you for reading the article Evaluate the expression a log 25 25 6 times 25 b 625 c log 2 25 d 2. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

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