Question

Can someone help me with understanding the change of base formula? I am supposed to find the logarithm using the change of base formula for this question log5to the power of 80?

Answer 1

Log (base 5) 80 ??

Answer 2

yeah

Answer 3

I guess I know how to switch the numbers over to replace in the formula but I keep getting large numbers when I put it in the calculator.

Answer 4

In change of base, You can Select any arbitrary base x (The Selection of x should be such that it helps in simplification)

and above Log(base5) 80 = Log (base5) 16*5 = Log (base5) 16 + Log (base5) 5 =

Log (base5) 16 +1 = (Log (base2) 16)/(Log (base2) 5) +1

Answer 5

=(Log (base2) 2^4)/(Log (base2) 5) +1 = (4Log (base2) 2)/(Log (base2) 5) +1 =
(4)/(Log (base2) 5) +1

Now I guess i am stuck at (Log (base2) 5).

so it all depends on the base to be chosen as in i chosed 2 here...

Answer 6

I am using the base of 10 would you be able to help me calculate log (base 10) 80 divided by log(base10) 5

Answer 7

Yes, You can separate the terms as in lets mark x= log (base 10) 80
and y =log(base10) 5

We solve the x first. 10^x =80
for y . 10^y =5

Answer 8

are you still there cuz I disconnected somehow but I see your answer. This is my first time trying this sight.

Answer 9

yeah I am here.Hmm Let me think a way out to solve this.

Answer 10

if:\[\log_ab=c\]then this implies:\[b=a^c\]do you understand that rule?

Answer 11

Hey I figured it out. Instead of trying to put it in the calculator as log base and # I was supposed to put it as ln(80)/ln(5) and I got the answer when I did that.

Answer 12

if you do, then you can use that result to derive the log to any other base.

Answer 13

yeah I do understand that part thank you for both of your help.

Answer 14

Hahaa...Ohh Yes If You Could Use the Calculator You should have told me..lol. I was trying to solve it without it.

And You gt the answer, because in Calculator every log is base to 10 or e(exponential)

Answer 15

Ive never done this before am I supposed to click best answer or something.

Answer 16

so taking the last result, if we take log to the base d of both sides (where d is the new base we want), then we get:\[b=a^c\]\[\log_db=\log_d(a^c)=c*\log_da\]therefore:\[c=\frac{\log_db}{\log_da}\]therefore:\[\log_ab=\frac{\log_db}{\log_da}\]

Answer 17

this is known as the change of base formula

Answer 18

I'm not here for medals - more for teaching - so feel free to award medal to whomever you feel like :)