Another logarithm question: If log base 5 of 12=a and log base 5 of 2 = b. Find log base 3 of 50 in terms of a and b.

[Helenam]

I need some help with this one please.
If log base 5 of 12=a and log base 5 of 2 = b. Find log base 3 of 50 in terms of a and b.
I started with the change of base formula to get log base 3 of 50 = (log base 5 of 50)/(log base 5 of 3) but now I’m stuck?

 

[Helenam]

I forgot to add that I found log base 3 of 50 = a-2b but cannot find a way to make 50.

 

[Helenam]

Oops sorry. I totally mixed up what I just wrote.
I meant that I found that log base 5 of 3 = a-2b. I just cannot figure out how to find log base 5 of 50.

 

[limiTS]

[imath]\log_5 50=\log_5(5\cdot5\cdot2)=\log_5 5+\log_5 5+\log_5 2[/imath]

And what is [imath]\log_5 5[/imath]?

 

[Helenam]

Ah! Thank you. I got so hung up on the values I could make with 12 and 2 etc I never thought of log base 5 of 5.