Logarithms: solve log_6n=3/4log_616

[wind]

Hi, I need help with this question

solve...

\(\displaystyle \L\\\log_{6}n=\) \(\displaystyle \L\\\frac{3}{4}log_{6}16\)
.
.
\(\displaystyle \L\\\ n=\) \(\displaystyle \L\\\frac{{0.75}log_{6}16}{log_{6}}\)

Do the \(\displaystyle \L\\\ log_{6}\) cancel out?

n=12?

 

[Unco]

Hi, I need help with this question

solve...

\(\displaystyle \L\\\log_{6}n=\) \(\displaystyle \L\\\frac{3}{4}log_{6}16\)
.
.
\(\displaystyle \L\\\ n=\) \(\displaystyle \L\\\frac{{0.75}log_{6}16}{log_{6}}\)

Do the \(\displaystyle \L\\\ log_{6}\) cancel out?

n=12?

\(\displaystyle \mbox{ \log_6}\) is an operation, not a number. Care to have a rethink?

 

[wind]

Care to have a rethink

...I don't know what to do :?

 

[skeeter]

\(\displaystyle \L \log_6{n} = \frac{3}{4}\log_6{16}\)

\(\displaystyle \L \log_6{n} = \log_6{16^{ \frac{3}{4}}}\)

note ... if log(a) = log(b), then a = b

\(\displaystyle \L n = 16^{ \frac{3}{4}} = 8\)

 

[wind]

note ... if log(a) = log(b), then a = b

ah, I forgot about that

Thanks, skeeter, Unco