NatalieLove Group Title Write log4 14 as a logarithm of base 3. 2 years ago 2 years ago

1. Pandae Group Title

tell your teacher this isnt helpful in the real world

2. NatalieLove Group Title

i don't have a teacher.

3. AccessDenied Group Title

logarithms can be helpful, depending on what you're actually doing in the real world. :)

4. Dockworker Group Title

$\frac{\log_{3}14}{\log_{3}4}$change of base

5. AccessDenied Group Title

i think if you're writing it just as a logarithm of base 3, you need one logarithm... which would also explain the excess work i was so confused by in class today (I had to do the same thing). :P

6. AnimalAin Group Title

Dockworker has it right, but such an answer isn't very practical, since the calculator, computer, and tabulated data are all for the common or natural logs.

7. AccessDenied Group Title

$\large{ \begin{split} log_4 14 &= log_3 x\\ \frac{log 14}{log 4} &= \frac{log x}{log 3}\\ 1.9037 &= \frac{log x}{log 3}\\ 1.9037~ log 3 &= log x\\ 0.9083 &= log x\\ 10^{0.9083} &= 10^{log x}\\ 10^{0.9083} &= x\\ 8.0965 &= x\\\\\\\\log_3 8.0965 = log_4 14 \end{split} }$ this is the process I am always asked to do to 'rewrite a logarithm with a logarithm of a different base

8. AccessDenied Group Title

Yes, it only says to rewrite using A logarithm, not a quotient of logarithms or just 'using the base 3' in which case the change of base would be sufficient...