Calculator gives wrong answers for log

Question

$10^3 = 1000$

My calculator with $10\log(1000)$ gives $30$

$15^4 = 50625$.

My calculator with $15\log(50625)$ gives $70.57$.

What am I doing wrong? Or would there be something wrong with my properties? I am using a Casio fx-82MS.

Thanks in advance,

Jarno

Well $\log(50625) \approx 4.704$ so your calculator is right. But your reasoning is not ! — Zubzub, Mar 09 '17 at 14:47
in the second line, you are multipying 10 by the number you want. log just means log with a base of ten. the 10 and 15 headers are unnecessary. — The Count, Mar 09 '17 at 14:47
$10Log(1000) = Log(1000^{10}) = Log((10^3)^{10}) = Log(10 ^ {30}) = 30$ — Cato, Mar 09 '17 at 14:48

score 0 · Accepted Answer · answered Mar 09 '17 at 15:20

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If you want the base-15 log of 50625, you need to calculate $(\log 50625) ÷ (\log15)$. If you do this you'll get the answer 4.

Similarly if you calculate $(\log 1000) ÷ (\log 10)$ you will get 3.

answered Mar 09 '17 at 15:20

MJD

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score 0 · Answer 2 · answered Mar 09 '17 at 15:25

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Your calculator interprets $10\log(1000)$ as $10$ TIMES $\log(1000)$, so $10$ times $3$. This is not completely unreasonable, given how $10x$ is short for $10$ times $x$ etc.

See the other answer for how to remedy this problem.

answered Mar 09 '17 at 15:25

Vincent

10,614

Calculator gives wrong answers for log

2 Answers2