Use the change of base formula to evaluate log (base 7) 76.

Question

tester97 · Answer

$$\log_{7} 76$$

zepdrix · Answer

Hmm I don't think 76 is any nice power...
So we can use a calculator for this one, yes?

tester97 · Answer

I get 64.22 when i do it with a calculator is that correct|?

zepdrix · Answer

Here is the rule we want to use:$$\Large\bf\sf \color{orangered}{\log_a(b)\quad=\quad \frac{\log_{10}b}{\log_{10}a}}$$We'll change them to log base 10 so we can throw it into the calc.

zepdrix · Answer

$$\Large\bf\sf \frac{\log76}{\log7}\quad\approx\quad ?$$

zepdrix · Answer

Hmm are you sure you put it into the calculator correctly? You should get a very very different answer.

tester97 · Answer

wait hold on let me try something else

zepdrix · Answer

$$\Large\bf\sf \log(76)\div \log(7)$$Make sure you use brackets to keep things organized.

tester97 · Answer

i get 2.22 is that correct?

zepdrix · Answer

yayy good job \c:/

zepdrix · Answer

Should round up to 2.23 I guess :P

tester97 · Answer

Yes finally today i get something correct thank you.