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Answer :
To solve the expression [tex]\(\log_5 3125 - \log_2 16\)[/tex], we need to evaluate each logarithm separately and then subtract the results.
1. Evaluate [tex]\(\log_5 3125\)[/tex]:
The expression [tex]\(\log_5 3125\)[/tex] asks the question, "To what power must 5 be raised to get 3125?" Since [tex]\(5^5 = 3125\)[/tex], it means that the answer is 5. Thus,
[tex]\(\log_5 3125 = 5\)[/tex].
2. Evaluate [tex]\(\log_2 16\)[/tex]:
The expression [tex]\(\log_2 16\)[/tex] asks the question, "To what power must 2 be raised to get 16?" Since [tex]\(2^4 = 16\)[/tex], the answer is 4. Thus,
[tex]\(\log_2 16 = 4\)[/tex].
3. Subtract the results:
Now, we subtract the two values we found:
[tex]\(5 - 4 = 1\)[/tex].
Thus, the result of the expression [tex]\(\log_5 3125 - \log_2 16\)[/tex] is [tex]\(1\)[/tex].
1. Evaluate [tex]\(\log_5 3125\)[/tex]:
The expression [tex]\(\log_5 3125\)[/tex] asks the question, "To what power must 5 be raised to get 3125?" Since [tex]\(5^5 = 3125\)[/tex], it means that the answer is 5. Thus,
[tex]\(\log_5 3125 = 5\)[/tex].
2. Evaluate [tex]\(\log_2 16\)[/tex]:
The expression [tex]\(\log_2 16\)[/tex] asks the question, "To what power must 2 be raised to get 16?" Since [tex]\(2^4 = 16\)[/tex], the answer is 4. Thus,
[tex]\(\log_2 16 = 4\)[/tex].
3. Subtract the results:
Now, we subtract the two values we found:
[tex]\(5 - 4 = 1\)[/tex].
Thus, the result of the expression [tex]\(\log_5 3125 - \log_2 16\)[/tex] is [tex]\(1\)[/tex].
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