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

Answer 1

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.

Answer 2

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.