How do you evaluate ${log}_{10} 10, 000$ $log_10 10,000$ ?

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Answer 1 · 2016-03-13T21:33:56

${log}_{10} 10, 000 = 4$ $log_10 10,000 = 4$

Given: ${log}_{10} (10000)$ $" "log_10(10000)$

Let $y = {log}_{10} (10000)$ $" "y=log_10(10000)$

Then another way of writing this is:

$10^{y} = 10000$ $10^y=10000$

But $10^{4} = 10000$ $10^4=10000$

So $y = 4$ $y=4$

Thus ${log}_{10} 10, 000 = 4$ $log_10 10,000 = 4$

Basically: count the 10's as $10, 000 = 10 \times 10 \times 10 \times 10$ $10,000 = 10xx10xx10xx10$

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