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NatalieLove
Write log4 14 as a logarithm of base 3.
tell your teacher this isnt helpful in the real world
i don't have a teacher.
logarithms can be helpful, depending on what you're actually doing in the real world. :)
\[\frac{\log_{3}14}{\log_{3}4}\]change of base
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
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.
\[ \large{ \begin{split} log_4 14 &= log_3 x\\ \frac{log 14}{log 4} &= \frac{log x}{log 3}\\ 1.9037 &= \frac{log x}{log 3}\\ 1.9037~ log 3 &= log x\\ 0.9083 &= log x\\ 10^{0.9083} &= 10^{log x}\\ 10^{0.9083} &= x\\ 8.0965 &= x\\\\\\\\log_3 8.0965 = log_4 14 \end{split} }\] this is the process I am always asked to do to 'rewrite a logarithm with a logarithm of a different base
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...