Logarithm Using Givens (without calculator)

Given $\displaystyle \log 2 = 0.3010$ and $\displaystyle \log 3 = 0.4771$ find $\displaystyle \log_5{512}$

I was only able to simplify to $\displaystyle 9\log_5{2}$, but I don't know what to do. I tried using the change of base formula, but that left me with $\displaystyle \log 5$ which I couldn't compute algebraically

Re: Logarithm Using Givens (without calculator)

Quote:

Originally Posted by

**ReneG** Given $\displaystyle \log 2 = 0.3010$ and $\displaystyle \log 3 = 0.4771$ find $\displaystyle \log_5{512}$

I was only able to simplify to $\displaystyle 9\log_5{2}$, but I don't know what to do. I tried using the change of base formula, but that left me with $\displaystyle \log 5$ which I couldn't compute algebraically

I think that there is a typo in the statement of the question.

I think the 5 should be a 3.

Re: Logarithm Using Givens (without calculator)

I wish that was the case, but it's not.

Re: Logarithm Using Givens (without calculator)

Quote:

Originally Posted by

**ReneG** I wish that was the case, but it's not.

Then that problem cannot be done. But I am willing to bet it is a typo.

Re: Logarithm Using Givens (without calculator)

I've figured it out $\displaystyle \log_5{512} = \frac{9\log 2}{\log{10} - \log 2} = \frac{9(0.3010)}{1-0.3010}$

I didn't need log 3 to solve it though.

Re: Logarithm Using Givens (without calculator)

Quote:

Originally Posted by

**ReneG** I didn't need log 3 to solve it though.

Nice work! However since you didn't need the log(3) I'm skeptical...

-Dan