Question

Write log4 14 as a logarithm of base 3.

Answer 1

tell your teacher this isnt helpful in the real world

Answer 2

i don't have a teacher.

Answer 3

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

Answer 4

\[\frac{\log_{3}14}{\log_{3}4}\]change of base

Answer 5

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

Answer 6

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.

Answer 7

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

Answer 8

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...