ln56/ln7=ln8. Is this true or is this false?

Question

anonymous · Answer

When I inputted them into my calculator. ln8 was not exactly as the same answer ln56/ln7 but it was very close. Would this make it true nonetheless? ln56/ln7=4.025/1.946=2.069. but ln8=2.047

anonymous · Answer

According to my calculator, it is false.

anonymous · Answer

Did you get different values? if I use log I get a different answer as well

anonymous · Answer

When you divide ln's, maintain the function and divide the terms.
Hence ln56/ln7=ln(56/7)=ln8, therefore, true.

anonymous · Answer

Interesting. Then 56/7 can be divided when next to ln?

anonymous · Answer

My calculator has In sign on so that's i got it's false.

anonymous · Answer

Wait, wait!! It is false!

anonymous · Answer

Please pay attention the following properties:

anonymous · Answer

$$lnA-lnB=\ln (\frac{ A }{ B })$$
$$lnA:lnB=\ln(A-B)$$
$$lnA*lnB=\ln(A+B)$$$$lnA+lnB=\ln(A*B)$$
Hence$$\ln56/\ln7=\ln(56-7)=\ln49\neq \ln8$$

anonymous · Answer

Ah, I see. I forgot to implement the logarithm rules. Thank you for very much. This is perfect

anonymous · Answer

No problem.