# Thread: Logarithm Using Givens (without calculator)

1. ## Logarithm Using Givens (without calculator)

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

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

2. ## Re: Logarithm Using Givens (without calculator)

Originally Posted by ReneG
Given $\log 2 = 0.3010$ and $\log 3 = 0.4771$ find $\log_5{512}$

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

3. ## Re: Logarithm Using Givens (without calculator)

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

4. ## Re: Logarithm Using Givens (without calculator)

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.

5. ## Re: Logarithm Using Givens (without calculator)

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

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

6. ## Re: Logarithm Using Givens (without calculator)

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