Is my answer correct?
Logarithm problem
If you can, please explain process

Question

elise_a18 · Answer

attachment

unklerhaukus · Answer

$$\log_b\left(\frac{A^5C^2}{D^6}\right)\
=\log_b(A^5)+\log_b(C^2)-\log_b(D^6)\
=5\log_b(A)+2\log_b(C)-6\log_b(D)\
=$$

elise_a18 · Answer

I did all of this through a calculator after plugging in the numbers but I got none of the answers...

unklerhaukus · Answer

What did you get?

elise_a18 · Answer

origionally I got -1.21

unklerhaukus · Answer

Can you show some working?

elise_a18 · Answer

i did exactly what you did in the last line of your post then I plugged in the numbers

unklerhaukus · Answer

$$\log_b\left(\frac{A^5C^2}{D^6}\right)\
=\log_b(A^5)+\log_b(C^2)-\log_b(D^6)\
=5\log_b(A)+2\log_b(C)-6\log_b(D)\
=5(3)+2(2)-6(5)\
=$$

triciaal · Answer

you said basics  
you do not need an electronic calculator
as shown above when you multiply numbers add the logs and when you divide numbers subtract the logs

elise_a18 · Answer

Where do the logs go? I don't follow :(

elise_a18 · Answer

I fixes it @triciaal, sorry I confused you

unklerhaukus · Answer

the value of the logs of A, C and  D are given in the question

elise_a18 · Answer

yes i know

triciaal · Answer

is everyone clear with everything now?

elise_a18 · Answer

i guess I don't understand why they're being multiplied by the exponent

unklerhaukus · Answer

This is a property of logarithms 
$$\boxed{\log_b x^n =n\log_b x}$$

elise_a18 · Answer

yes but why are you multiplying  and exponent

unklerhaukus · Answer

huh?

unklerhaukus · Answer

we had to move the exponents out of the logs,
 because the log values we were given didn't have and exponents

elise_a18 · Answer

ohhhhh okayy. Sorry I get it now. I was just overthinking it lol

unklerhaukus · Answer

ok!