is this right?

Question

i had to make log(5)17 a common log with a base of 10..

so ...i made it 10^(log(5)17) which is log X = log (5)17 which is log X = 1.760. is that the same thing as making hte equation a common log??

Answer 1

NB.
You have to change the log base from 5 to 10; the equation below is the general equation for changing log bases.
log(a)b = log(10)b divided log(10)a
Hence
log(5)17 = log(10)17 / log(10)5
By algebraic manipulation :-
log(5)17 x log (10)5 = log(10)17
OR :-
log(5)17 = log(10)17 / log(10)5
-" - = 1.230448921 / 0.698970004
-" - = 1.760374428
-"- = 1.760

1.760 is the logarithmic value of 17 using base 5. It is NOT the logarithmic value of 17 using base 10.
I hope this helps!!!!

Answer 2

Yes, sort of. You solved for the common log, so it's technically correct.

The easier way to do it is

log # / log base

So, in your case:

log 17 / log 5

Which does equal 1.760, so that works.