Question

IMPORTANT: Need help with logarithms, am posting question with equations below. Medal to anyone who helps!

Answer 1

Okay, so the question is, "Use change of base formula to find three significant digits."
Here is the starting equation.
\[\log_{x}y=\frac{ \log_{b}y }{\log_{b}x }\]
The problem they want me to answer is \[\log_{2}6+\log_{3}5 \]
Using the change of base formula, I plugged my info in and got \[\frac{ \log6 }{ \log2 }+\frac{ \log5 }{ \log3 }\]
What I'm wanting to know is if, one, I set this up correctly, and two, if I can add the logs and if so how can I add the logs?

Answer 2

@whpalmer4

Answer 3

Okay, assuming you can compute or look up common logs (base 10), then yes, you have written this correctly and should be able to evaluate it now.

Answer 4

What would be my next step?

Answer 5

An interesting point is that it doesn't matter which log base you use for calculating the logs in the change of base formula: you've written it with the common log, but in fact you'll get the same answer if you do it with \(\log_{57}\), \(\ln\), or whatever you fancy :-)

Answer 6

Bust out your calculator or go to a website which offers one and evaluate those logarithms. Or ask your friendly helper who memorized those values a few decades ago :-)

Answer 7

Would I turn them into fractions?

Answer 8

yes, but you have to find the values of the logs first

Answer 9

\[\log 2 \approx 0.30103\]
there's one to get you started :-)

Answer 10

do you have a calculator handy with a logarithm button?

Answer 11

\[\log 3 \approx 0.47721\]

By the property of logs, we can use that to find \(\log 6\)

\[\log a + \log b = \log(a*b)\]We know the values of \(\log 2\) and \(\log 3\), so \[\log 6 = \log(2*3) = \log 2 + \log 3 \approx 0.30103 + 0.47712 \approx 0.77815\]